I looked at some sources about the Greek-Turkish war and found something I didn't know. Crete similarly had a large Turkish population but the treaty ending the war provided for an exchange of populations and they were sent to Turkey. Cyprus, not part of Greece, was not part of that agreement.
There seem to be some serious moves to cut a peace deal there. What's happened since the Turkish occupation of the north end is the Greek area got it's act together and got into the E.U. while the Turkish government in the north is a pariah. The Greeks are getting rich while the Turks stagnate in a territory where you can't even fly nonstop, except from Turkey.
Old animosities die hard. The Turks refuse to open her ports to ships from Cyprus and hence, Turkey’s accession into the EU trundles on ...apparently Sarkozy does not want them in ... but Greece remains an ally in that regard.