Aliens in N register
It used to be you set up a corporation, often in DE to do this. There a several companies that specialize in this and it was reasonably cheap. Lots of Europeans do this. It lets you exercise the FAA IR privileges in Europe among other benefits. Posting on the private flying forum will get better info particularly, from IO-540 who is pretty knowledgeable about this.
The big, bad news is, the FAA has recently apparently stopped accepting these registrations. There has being a very serious, post 911, tightening of registration compliance in the last few years and this seems to be part of it.
You might look at the AOPA web site to check the latest.
I suggest you proceed with extreme caution.
20driver