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Why say that? A simple google of "cyprus chechnya terrorist training turkey" leads to articles dating back to 2000 from sources as varied as The WP, Pravda, VOA and DoJ that make the same allegations.
Russia and turkey are long-time enemies and turkey has been training military from former USSR states since the dissolution, as well as pushing to extend its oen sphere of influence into the oil fields of the Caucucus.
I stand by my original assesment. Northern Cyprus has made heaps in recent years as far as integration goes. In fact, were it not for the Cypriot Greek vote a few months back, they could very likely be in the EU already. In light of all that I find it implausible that Cypriot Turks would get involved with any Chechen terrorists. Same goes for Turkey proper.
I followed the links you gave and I only found one article related to the subject, it was the Pravda article. Pravda is on par with National Enquirer, as far as I'm concerned.