I was told by a GC living here in the RoC (who has a UK passport) that even if he wanted to buy anywhere to live in the North he couldn't on account of him having a 'Cypriot' name. And nor could his wife, who is British, on account of her having a Cypriot name too (his of course!)
Isn't there some restriction on length of stay (3 days?) on GCs going across to the North?
Read that somewhere but it might be out of date now.