There's only one place on earth that H. sapiens is "native" to, and that's the Garden of Eden (or Africa's Great Rift Valley, depending on your belief system).
Unless you're still living where your ancestors came from, you're an immigrant. If any Hominids originated in the Americas, we have yet to discover their remains. Ergo all Hominids living in the New World are immigrants, Indians included.
Uh, I’m a native American — America’s very name is from a Renaissance-era Italian, and I was born here. Anyone born in the Americas is a native American.