Grill-able middle eastern cheese?

I order vegetarian kebabs (called gyros in the US) all the time, and I want to make them on my own at home (much healthier, since I can use less oil!) ,but I cannot figure out for the life of me what type of cheese they use. It is cubed up, and then when placed on the grill, it browns on the outsides but doesn't melt. It amazes me, really. Anyone know what kind/kinds of cheese can be used for this? Thanks in advance!