I think you implicitly assume adaptation meaning losing someone's identity with his/her own culture.

Those two things are not mutually exclusive, IMO. Quite on the contrary, I think in order to successfully adapt, you have to know where you stand in the first place. What fits you, what does not. It is an ever-going process, long and sometimes painful. But in the end, it will force you to better understand your own background, its virtue and weakness alike, and what difference has America bringing to it.