Okay, the time at last has come to ask the big architectural questions about the National Museum of the American Indian, opening on Tuesday.

Basically, they are three: Is the architecture any good? Does the building fit the Mall? And who did the design?

If this last question strikes you as odd, you can rest assured -- it is odd. However, let's take the questions in order.

It is pleasing to report that the architecture is very good, and quite strange. The building rises above the elm trees of the Mall like a monumental apparition. Its curving walls shout, "Look at me!" And the more you do, the more there is to see and think about.

Even more satisfying is the conclusion that, physically and philosophically, the new building creates a strong, tension-filled dialogue with its setting, and carries it off with amazing grace.

But whom to credit for this good work? That's another question entirely. Uncertainty as to authorship of the whole and its parts -- especially the parts -- is one of the haunting curiosities of this building.

We know that Douglas Cardinal, the Indian architect from Canada well respected for his signature "organic" works, is the creative intellect behind the building.

Yet Cardinal and his U.S. collaborators were fired by the Smithsonian Institution in 1998, about halfway through the design process. It is thus hard to tell exactly who is responsible for what, especially on the inside. The reasons for this make a sad, messy story.

Fortunately, back in 1999 the Commission of Fine Arts stepped in to block ruinous design changes proposed by the Smithsonian after Cardinal's dismissal, so it is possible to say with certainty that in the big, bold moves -- the shape, the character, the basic floor plan -- this building is a Cardinal.

You can tell this by scanning the architect's history. Masonry curves are what Cardinal does. They have been the keys to his artistic identity since 1968, the completion date of his first major building, St. Mary's Roman Catholic Church in Red Deer, Alberta. It's a small building with astounding curved brick walls.

Cardinal's vocabulary of curves may have something to do with the landscapes he absorbed during his boyhood in western Canada. Likewise, his connection to his Native American roots -- Cardinal is Blackfoot and Metis -- played its part.

Mainly, though, this signature style evolved from Cardinal's almost mystical identification with nature. He speaks of the architect's role as a revealer of forms that are inherent in a particular site. He refers to the Washington building as a "spirit mountain," a stone building that is "an abstraction of the rock that formed this continent."

Sometimes, in organic architecture, this kind of thinking produces buildings that really do seem to grow from the site, or to complement it in compelling ways. Frank Lloyd Wright's Fallingwater in the Pennsylvania forest is a paramount example.

But Cardinal likely would consider Wright's lyricism too literal. For him, organic architecture is more a matter of metaphysical principle -- architecture harnessing and expressing a life force.

The new building on the Mall, in any case, definitely does not feel as if it "grew" from this particular piece of land. A long time ago, before colonization, the site (between Jefferson Drive, Maryland Avenue and Third and Fourth streets SW) was a little woodland next to a creek. Yet the references in Cardinal's architecture aren't local. They're not even Appalachian. The building brings to mind the mountains and the ancient native architecture of the American Southwest.

However, accepting the artifice is something one does willingly because the architecture is so convincing. As a romantic abstraction of nature, this building really works.

It is a powerful form. Those dramatic cantilevered bands above the entrance are scintillating when seen from afar, like some natural wonder you might see in New Mexico. And when you stand far beneath the cantilevers in the museum's circular forecourt, the scale has an almost physical effect. You feel both overwhelmed and sheltered. I can't think of another architectural space quite like it.

Then there is the way those blocks of rough-cut dolomitic limestone on the wavy walls react to the sun. They love it, all day long. And it loves them. Strong shadows enliven the surfaces of the big building. And the warm earth tones, rare in Washington, add a rich new note to the Mall's palette.

The building affects your spirit. It is intimidating but also exhilarating. These opposing reactions bespeak the tension built into any effort to make a monumental building that's an obvious abstraction of natural forms or forces. It is a risky thing to do, but Cardinal makes it work here, as he did in Ottawa with the Canadian Museum of Civilization, because he did not try to imitate nature.

Rather, he set up a series of contrasts between the nature metaphor and the material reality of the building. Those blocks of limestone, for instance, do indeed suggest a mountain's rough edges. But you can't help noticing that the stones are beautifully laid in irregular courses. You can feel the masons' touch.

More subtly, you can see and sense the human intellect behind the shaping of this building. Those curves are elegant and complex. They were conceived by a sensitive, daring brain, and could have been built only with the aid of advanced computer technology.

If this makes the architecture sound like High Seriousness and no fun at all, I should dispel this impression right away. The building is, quite simply, pleasant to be around.

Strolling along the paved walkway that curves gently away from Jefferson Drive is a Sunday treat. You can sit down in the shade. Listen to the water coursing nearby. Gaze up at the building's sensational north elevation. Even false notes such as the waterfall on the northwest corner -- it rings a Disneyland bell -- do not spoil the effect.

Efficiency experts might complain that the east-facing entrance is on the wrong side because the vast majority of the museum's visitors will arrive from the west, from the direction of the Air and Space Museum and the Smithsonian and L'Enfant Plaza Metro stations. And they'd be right. A west-facing entrance would have been a tad more convenient.

Then again, visitors would miss that pleasant walk! And, more to the point, an entry facing the rising sun was a key desideratum for members of the many tribes that took part in the lengthy consultations leading up to a design. This was a native characteristic everybody agreed on.

The eastern entryway might also be called the psychological key to the design, for it engenders a face-off with the U.S. Capitol up on the Hill. The view of the great Capitol dome from the entry plaza or the broad windows of conference and reading rooms is truly unforgettable. Symbolically, for Native Americans, what could be more powerfully poignant, or vindicatory, than that?

Unfortunately, the inside of the building doesn't quite live up to the outside. The intention clearly was to make the interior spaces thrilling and meaningful in the same ways, but they just don't have the same complexity and carry.

Unhappily, it's impossible to say precisely why. It may have been the absence of Cardinal's guiding hand in the design follow-through. Budget constraints possibly played a role. Perhaps it was the concept itself. Such uncertainty became a certainty the day Cardinal was fired.

The main public space, called the Potomac, is a vast domed chamber almost immediately behind the front doors. You enter it after passing by a large, semicircular fence woven from strands of copper. It's a wow space, 120 feet high from circular hardwood floor to the tension-ring skylight at the apex of the dome.

Conceptually, this space is a cross between the triangulated atrium of I.M. Pei's National Gallery East Building directly to the north across the Mall's greensward, and Thomas U. Walter's Capitol rotunda. Like the Pei atrium, it's an exciting center of movement, of going from here to there. Like the Capitol rotunda, it is a symbolic and ceremonial centerpiece.

But even though it impressively combines elements of both, the Potomac is not quite as dynamic as the Pei atrium, nor as convincing a symbolic focal point as the Capitol rotunda. These two civic interior spaces are the best of the best in Washington, and the Potomac isn't quite on par.

Perhaps the room is just too big and empty. The scale is somehow off. All that wallboard doesn't help -- when you look up, the concentric rings of the dome look a bit flimsy. Strangely, the center point of the tension ring in the dome skylight doesn't align precisely with the center of the ceremonial floor. That woven copper fence just seems a bit fussy, a bit off. It all adds up to a disappointment.

Still, the space definitely has a distinctive allure. Crowds will pep it up a lot, as they do in Pei's space. The best place to watch it all happen will be the balconies at the third and fourth floors. Behind you are the exhibition spaces, and all around is a fascinating play of curves. There's an interesting, yin-yang contrast between the flowing, irregular curves of the lower floors and the dome's concentric rings.

Native American ceremonies and performances will take place in the Potomac, and also outside the building, on that circular entry platform and in an intimate amphitheater snuggled next to the north facade. These will sanctify the spaces for the building's primary users, and make things a lot more interesting and meaningful for the rest of us.

Throughout, there are wonderful inside-outside exchanges. The views of the Capitol from the double-height third-floor reading room. The windowed alcoves at the end of wavy hallways. The window tables in the ground-floor cafe, with gently falling water outside. I'm no fan of the cafe decor -- it's sort of Class A food court design -- but these are the best seats in the house.

Decor is what happened to several of the interiors. The ground-floor auditorium, for instance, is a nice, rounded, intimate performance space with 340 seats, but the design narrative -- a clearing in the woods under a night sky -- is as thin as the wooden battens stuck on the walls.

No question, though, that this is a welcoming building. Cardinal once spoke of it as a sheltering cave, and it's a terrific cave. There's plenty of openness but also a lot of warmth. Woods are skillfully deployed. You want to reach out and touch the hand-adzed wooden walls of the Roanoke, the museum store on the second floor.

Nor is there any doubt that this strange, magnificent artifact is a welcome addition to Washington, and to the Mall.

The scale of the Mall, after all, is grand enough to embrace a bit of difference. Actually, a lot of difference. The symbolic greensward establishes an indelible order. But behind those stately elms the Mall is a parade of architectural individuality.

To build on the Mall, you just have to follow a few simple rules about height and setbacks, which Cardinal did, and then do your best, which he also did until the spring of 1998. Thanks largely to those efforts, the new museum adds a poignant, provocative, strangely elegant note to the national parade.

In form, the museum evokes not its Eastern setting but the Southwest. Its architect saw it as "an abstraction of the rock that formed this continent."Sidewalks around the Indian Museum are inlaid with celestial patterns, such as this one near the south entrance.The Potomac space is a vast domed chamber 120 feet high from the hardwood floor to the skylight at the apex of the dome.The National Museum of the American Indian is a medley of cantilevered curves, a structure simultaneously intimidating and exhilarating.