I'm looking for advice for the following:

One of our PIs, with an NSF grant, wants to hire a Ph.D. grad student
from the U.K. to work on his project.  This would be someone who will
not be a grad student as recognized by our graduate school (thus
entitled to institutional tuition remission, stipend and health
insurance).  But the PI wants to provide a stipend and tuition at the
student's home institution.

Is this feasible? Or, are there other alternatives?  I don't see
anything in the NSF guidelines that helps me understand.

Thank you!

Tim