Michael Stebbins in “I Am My Own Wife” by Doug Wright at Rep Stage. (Stan Barouh)

Doug Wright’s “I Am My Own Wife” premiered in New York in 2003, appeared at the National Theatre in 2005, was produced by the Olney Theatre Center in 2007 and Baltimore’s Everyman Theatre in 2009, and now it’s being done at Columbia’s Rep Stage. The old gal gets around.

The reasons are clear: It’s an impressive showcase for any actor who can play the solo show’s dozens of roles. And the true story is a doozy, about a seemingly modest German transvestite (and major antiques collector) born Lothar Berfelde but eventually known to the world as Charlotte von Mahlsdorf, who somehow survived both the Nazi and then the communist East German regimes.

That one-two punch made the play a major curiosity when it emerged, earning Wright a Tony and a Pulitzer, with best actor honors for original star Jefferson Mays (who then toured nationally with the show). It’s less splashy but reasonably effective at Rep, although director Tony Tsendeas puts almost all of the storytelling duties squarely on Michael Stebbins’s shoulders.

As Charlotte (pronounced Shar-lotta), Stebbins wears the obligatory plain black dress, kerchief and orthopedic shoes, plus a simple strand of pearls. He creates the show’s gallery of characters with voices and accents, moving easily enough from German inflections (“otherwise” sounding like “uzza-vize”) to a gentle drawl for the Texan Wright.

Wright’s 1990s journals and interviews with Charlotte are the spine of the story, and it’s an odd bit of hero worship. Wright, who is gay, finds Charlotte’s survival tales inspiring, but things take a twist when he learns that some of those tales may be too good to be true. This is the only part of Stebbins’s performance that nags a little; you wish he could find some rougher textures as Wright — here played as a kind of put-upon saint — grows more conflicted about his maddeningly slippery subject.

More troubling is the lack of urgency and showmanship in the Rep’s staging. Previous productions of “Wife” dramatically featured grand stacks of the furniture and phonographs Charlotte collected, but Tsendeas and set designer Elizabeth Jenkins McFadden forgo that. Stebbins only has miniatures to handle as Charlotte rhapsodizes about one collectible or another, and although a few small frames at the back of the simple living room set glow with artifacts, it’s not enough.

The show even seems short on sound and light to help animate the plot (which is not especially propulsive here) and to more richly suggest the enforced norms and shadowy resistance inside Charlotte’s hazardous Germany (and inside her perplexing head). For all its one-man flamboyance, the play is a self-scrutinizing documentary, and it needs more than a capably chameleonic performance to drive it home. It wants the weight of real history.

I Am My Own Wife

by Doug Wright. Directed by Tony Tsendeas. Lights, Jay Herzog; costume design, Jennifer Tardiff; sound design, Neil McFadden. Through Nov. 17 at Rep Stage, Howard Community College, 10901 Little Patuxent Pkwy., Columbia. About two hours. $15-$40. Call 443-518-1500 or e-mail boxoffice@howardcc.edu .