California Gov. Arnold Schwarzenegger (search) has much to offer President Bush and the GOP when he appears at this week's Republican convention, from unmatched star power to moderate politics that appeals to voters outside the Republican base.

Schwarzenegger also stands to gain some political gravitas and a debt of gratitude from the party that could pay dividends for California.

But there are risks on both sides. Schwarzenegger could tarnish his bipartisan image by aligning himself with a president and party that are unpopular in his home state, while Bush risks getting overshadowed by a one-of-a-kind star who doesn't always stick to the script.

"It's a challenge to write a speech for Schwarzenegger because his real strength and charisma comes as the political outsider fighting the demons, fighting the dragons," said Barbara O'Connor, director of the Institute for the Study of Politics and the Media (search) at California State University, Sacramento. "And he can't fight the dragons there. He has to support the dragons."

Schwarzenegger will speak Tuesday during prime-time, a plum spot that guarantees live coverage on network television. Aides said he will give a personal, 15- to 20-minute speech about his evolution from Austrian bodybuilder to Hollywood movie star to Republican governor, and that he'll be effusive in his support for Bush.

"He doesn't want to send them a particular message other than to share what he's shared with voters in California as to why he's a Republican, and to give a personal story of why he's chosen to be in the Republican Party," said spokesman Rob Stutzman.

Stutzman said the White House didn't vet the speech, but "I believe they're very pleased, as are we — looking forward to this being a real landmark event in the governor's young political career."

Schwarzenegger took office last November after voters recalled Democratic Gov. Gray Davis. He has remained wildly popular even as bruising battles with the majority-Democrat legislature saw him break his promise to deliver an on-time state budget.

Now he has a chance to position himself as a national political leader — though the one topic he almost certainly won't discuss is whether he himself might one day run for president. That would require amending the Constitution to allow foreign-born citizens to be president, which Schwarzenegger is on record supporting.

"What he gets out of it, I think, is a chance to show that he's done this on more than just a whim, at least to show the rest of the country," said convention delegate Mark Leyes, a city councilman in Garden Grove, Calif. "That he can do it with a good nature and good sense of humor as well, but that he's as serious a politician as anybody."

But Schwarzenegger must proceed carefully in declaring his support for Bush, since he, and most voters in Democrat-leaning California, differ with the president on issues from gay marriage to oil drilling. Schwarzenegger's approval rating stood at 65 percent in California in a poll this month, while Bush's was 40 percent.

So far, Schwarzenegger's embrace of Bush's re-election effort has been cautious. They've appeared together in the state but the governor has sent mixed signals about campaigning outside California for Bush. GOP leaders insist Schwarzenegger runs no risk by appearing for Bush, but some party activists see it differently.

"He's going to do the right thing for the president, but he has everything to lose and nothing to gain," said convention delegate Mark Leggio, a Southern California auto dealer. "He can be characterized as a Republican, a far-right extremist, a pro-Bush guy. There's so much Bush hatred out there."

Most analysts expect Schwarzenegger to ignore areas of difference with the president, and instead focus on Bush's leadership qualities as well as his own personal story. GOP leaders hope Schwarzenegger can use the huge television audience he's certain to attract to sway fence-sitting voters with his optimistic, moderate image and immigrant success tale.

"His own life story is representative of what the Republican Party stands for, namely the ability for an immigrant to legally come to this country with little and succeed," said Gerry Parsky, chairman of the Bush-Cheney campaign in California and of California's convention delegation.

Schwarzenegger will also use his time in New York to visit an after-school program in Harlem, hobnob with donors, and make a red-carpet entrance to a lunch at Planet Hollywood. But analysts cautioned that, while it's hard to overshadow a president at his own convention, the governor who loves the spotlight must use it, this time, to promote somebody else.

"The question for his speech, as for any speaker, is what's the sound bite going to be. And if I were the Bush folks, I'd want the sound bite to be about George W. Bush, not about Arnold Schwarzenegger," said Arnold Steinberg, a Los Angeles GOP strategist. "I think that he has to rise above his superstar status and his charismatic political style so that he is seen also as a team player."