On this island we speak Greek for 1000s of years and then you come here to tell us that Cyprus is not Greek. So if the population of a territory is Greek, then how can the territory not being Greek? To whom the territory belongs to then? To some foreign rulers?
When you talk about murders and genocides you are obviously confusing it with the actions of the Turks.
First Greeks in Cyprus:
After 1400 B.C., Mycenaean and Mycenaean-Achaean traders from the northeastern Peloponnesus began regular commercial visits to the island. Settlers from the same areas arrived in large numbers toward the end of the Trojan War (traditionally dated about 1184 B.C.). Even in modern times, a strip of the northern coast was known as the Achaean Coast in commemoration of those early settlers. The newcomers spread the use of their spoken language and introduced a script that greatly facilitated commerce. They also introduced the potter's wheel and began producing pottery that eventually was carried by traders to many mainland markets. By the end of the second millennium B.C., a distinctive culture had developed on Cyprus. The island's culture was tempered and enriched by its position as a crossroads for the commerce of three continents, but in essence it was distinctively Hellenic.
First Turks in Cyprus:
Throughout the period of Venetian rule, Ottoman Turks raided and attacked at will. In 1489, the first year of Venetian control, Turks attacked the Karpas Peninsula, pillaging and taking captives to be sold into slavery. In 1539 the Turkish fleet attacked and destroyed Limassol. Fearing the ever-expanding Ottoman Empire, the Venetians had fortified Famagusta, Nicosia, and Kyrenia, but most other cities were easy prey.
In the summer of 1570, the Turks struck again, but this time with a full-scale invasion rather than a raid. About 60,000 troops, including cavalry and artillery, under the command of Lala Mustafa Pasha landed unopposed near Limassol on July 2, 1570, and laid siege to Nicosia. In an orgy of victory on the day that the city fell--September 9, 1570--20,000 Nicosians were put to death, and every church, public building, and palace was looted.
http://lcweb2.loc.gov/frd/cs/cytoc.html