Donald Trump addressed the GOP convention in Cleveland on July 21. The Republican presidential candidate spoke for more than an hour, but we break it down to less than five minutes. (Deirdra O'Regan/The Washington Post)

— A traumatized Republican Party came here hoping for an arena-size group therapy session.

The GOP at large would talk through its differences, remind itself of what it shares, then head into the fall election with a renewed sense of identity.

Instead, the week laid bare the fact that the party has become a collection of warring tribes, with no coherent set of principles beyond a burning desire to keep Hillary Clinton out of the White House.

The question many have is whether Donald Trump — with his skepticism of free trade and internationalism, blurry record on social issues, and insensitivity toward the life experiences of minorities — now owns the Republican Party or whether he is just borrowing it until November.

“I think the party is either in a major transition or in the throes of self-destruction,” said Randy Corporon, a Colorado delegate and tea party leader attending his first party convention.

Wednesday night’s eruption on the convention floor, when Sen. Ted Cruz (R-Tex.) took the stage and refused to endorse the celebrity billionaire who had bested him in the primary race, was the most dramatic expression of the party’s existential crisis.

On what was supposed to be a victory lap the day after his acceptance speech, Trump was still fixated on the snub by Cruz.

“I don’t want his endorsement,” Trump said during a rambling, disjointed news conference Friday morning. “If he gives it, I won’t accept it.”

Rather than turning his attention to the battle ahead, Trump revisited some of the low points of his primary fight: He defended his retweet of an unflattering picture of Cruz’s wife to his millions of Twitter followers. And he called attention to a false and far-fetched tabloid claim that Cruz’s father might have had a hand in John F. Kennedy’s assassination.

Trump also insisted that the quadrennial GOP gathering had been “probably one of the most peaceful, one of the most beautiful, one of the most love-filled conventions in the history of conventions.”

Mixed messages

Whatever its artistic merits, the convention had more than its share of dissonant moments.

Milwaukee County Sheriff David Clarke told the gathering Monday night that the Black Lives Matter movement represents “anarchy” and “a collapse of the social order.”

On Wednesday, however, another African American, Lynne Patton, who runs Eric Trump’s foundation, stood on the same stage and declared: “There’s not one person in this room who can deny that, historically, black lives have mattered less. My life mattered less. And whether we like it or not, there are people out there who still believe this to be true.”

On Thursday, billionaire Pay­Pal co-founder Peter Thiel became the first person ever to proclaim his homosexuality to a GOP convention audience, saying: “I am proud to be gay. I am proud to be a Republican.” During his nomination acceptance speech minutes later, Trump declared that he would protect ­“LGBTQ citizens,” prompting widespread applause in the hall.

Yet speaking earlier that same night was Tony Perkins, head of the Family Research Council, which argues that the rationale for same-sex marriage could also be used to justify man-horse matrimony. The GOP platform approved this week maintains opposition to same-sex marriage and argues in favor of allowing discrimination against gays for religious reasons.

The rifts extend into foreign policy as well. In an interview with the New York Times, Trump said he would condition assistance to NATO allies on whether the United States was “properly reimbursed” for the cost of its military operations — an abandonment of NATO’s core tenet as a mutual-defense organization.

“I think he’s wrong on that,” Senate Majority Leader Mitch McConnell (R-Ky.) told Politico. “I don’t think that view would be prevalent or held by anybody he might make secretary of state or secretary of defense.”

And while the convention approved the party’s most socially conservative platform ever, Trump has played down cultural issues in his campaign and did not mention abortion or God in his acceptance speech.

The GOP nominee did express gratitude to his evangelical supporters. “It is an easy decision to support Donald Trump over Hillary Clinton,” said David Lane, who heads the American Renewal Project, which mobilizes conservative pastors and hosts rallies in battleground states.

But he added: “Trump needs to give Christian voters a clear reason to vote. Otherwise, they will stay home.”

The convention also saw a few stray issues cross the stage. Trump’s daughter Ivanka, who gave the introduction to his acceptance speech Thursday night, promised that her father would rewrite federal labor laws to ensure equal pay for women and would “focus on making quality child care affordable and accessible for all”— two proposals espoused by Democrats.

Grass roots vs. elites

Trump’s rout of a highly credentialed field of 16 other candidates in the GOP primary contest revealed a chasm between the party’s passionate grass roots and the elites who have run its presidential selection process for decades. Much of that energy comes from insurgent forces such as the tea party movement, which was instrumental in giving Republicans their biggest House majority since 1929.

Specifically, Trump proved that it is possible to win a strong plurality of the vote with an appeal to nativism and bigotry, if it is dressed up as a backlash against “political correctness.” Moreover, it is now clear to party leaders that the clinical, by-the-book conservatism espoused by the GOP establishment has been insufficiently responsive to the economic concerns of working-class Americans.

Grover Norquist, the president of Americans for Tax Reform, said he would support Trump and suggested that his success proved that Republicans need to find new ways to talk about trade. However, Norquist said Trump’s foreign policy ideas, such as a temporary ban on Muslim immigration, are unlikely to endure.

“His vice president said that’s a dumb idea, the speaker of the House said that’s a dumb idea. And he backed off of it,” Norquist said. “Do we easily and quickly get a guy who went out too far on something to admit he was wrong? No.”

On Wednesday, Norquist held a roadshow version here of the popular conservative open-mic sessions he presides over in Washington. Trump was rarely mentioned; a succession of governors and strategists discussed the election as if another candidate sat atop the ballot.

“There’s a conservative House and Senate, and everyone’s focused on a presidential race that’s sui generis,” Norquist said. “If there were Trump candidates running for office, it would be one thing. But it’s not a wing of the party. It’s a guy.”

While many Republicans say they are skeptical that Trump can win in the fall, they say he has launched a struggle over the party’s identity that is likely to endure.

“There’s a real debate going on. A lot of people are already looking past November to see where the party goes next. There is a concern it will shrink further and double down on Trumpism,” said Alex Conant, a strategist who advised the failed presidential campaign of Sen. Marco Rubio (R-Fla.).

Looking to 2020

Even if Trump wins — but especially if he loses — the 2016 convention is likely to be remembered as an early proxy fight for the 2020 primary. The Cruz meltdown, while damaging in the short run, may look in retrospect like a principled stand. Meanwhile, Ohio Gov. John Kasich, another of Trump’s defeated primary opponents, kept an antiseptic distance from the convention proceedings in his own state, maintaining that his sunny brand of conservatism ultimately will prevail.

Throughout the chaotic week, anxiety percolated through the Republican donor class. They were heartened by Trump’s choice of running mate, Indiana Gov. Mike Pence, a popular and familiar figure.

But the face of the party is now Trump.

“I still have reservations about him as a person,” said Betsy DeVos, a major donor from Michigan, who attended the convention as a delegate. “I cannot and will not support and vote for Hillary Clinton. But I think there are things I want and personally need to hear [from Trump], and that is a more serious focus on the really critical and important issues of the day, and a demeanor that I think would reflect the office of the presidency.”

There is cautionary precedent for this week’s dissonance.

In 1964, the liberal Nelson Rockefeller was booed off the stage when he denounced extremism at the GOP convention in San Francisco. The nominee, Barry Goldwater, lost the election in a landslide.

In 1980, the Democratic convention was dominated by divisions between the incumbent, Jimmy Carter, and his liberal challenger, Sen. Edward M. Kennedy (D-Mass.). Kennedy gave a fiery speech, declaring that “the dream shall never die,” and party officials had trouble getting him to pose with the president for an onstage photo op.

That, too, proved to be an omen. Carter got trounced by Ronald Reagan, and Democrats lost the next two presidential contests by huge margins, as their liberal and centrist wings battled over the future of the party.

Then, as now perhaps, a convention set off a party’s struggle to find its soul.

Jenna Johnson, David A. Fahrenthold, Matea Gold, Tom Hamburger and David Weigel in Cleveland contributed to this report.