Can an aircraft on loan in the US be based outside the US?
Any US-registered aircraft can be based in any country subject to that country's rules. Just check with your local aviation authorities in the country where you want the aircraft to be based before you reposition the aircraft. Some may require you to depart the country every so many days/weeks/months, sometimes in as simple a way as a short hop across a border, but to my knowledge most don't have any restrictions.