How can the Republican Party attract more minorities, especially Asian-Americans?

According to Gallup, non-Hispanic whites are the only major racial/ethnic group that identifies as Republican, and even then just barely:

Group           Republican         Democrat

White                    45                         43

Black                      8                          83

Hispanic               21                         53

Asian                      24                        61

Given that whites are a rapidly shrinking portion of the population, the Republican Party stands no chance of long-term success unless it can radically change these numbers.  Personally, I’m most surprised at the Asian-American numbers.  I would have thought that Asian-Americans, with a history of hard work and little history of dependence on government would be an ideal recruiting ground for Republicans.  Yet the vast majority of Asian-Americans have rejected the Republican Party.  Why?  And what can be done about it?

I asked a similar question once before, and it led to a very interesting discussion about the history of the party — A Republican freed the slaves, MLK was a Republican until the Goldwater candidacy, etc.  However, I believe the general public is not much interested in history.  We live in a what-have-you-done-for-me-lately world.  What can Republicans offer, going forward, that all racial groups, especially Asian-Americans, are likely to embrace?