In the U.S. - no problem. In Canada you can't. Even though you can fly a N-numbered airplane there. Go figure.
Buy basically yes, you have to import it (no dues if it's US made, just broker fees or do your own legwork), I believe the owner up there needs to get an export certificate of airworthiness (their fed comes out, makes sure that the aircraft is a/w according to Can and US regs and issues a piece of paper), based on that our fed comes out and issues the new certificate of airworthiness.
Registration is simple, just fill out the application for registration. But the above needs to be done first.