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We prove the existence of invariant almost complex structure on anypositively omnioriented quasitoric orbifold. We construct blowdowns. We defineChen-Ruan cohomology ring for any omnioriented quasitoric orbifold. We provethat the Euler characteristic of this cohomology is preserved by a crepantblowdown. We prove that the Betti numbers are also preserved if dimension isless or equal to six. In particular, our work reveals a new form of McKaycorrespondence for orbifold toric varieties that are not Gorenstein. Weillustrate with an example.

Almost complex structure, blowdowns and McKay correspondence in quasitoric orbifolds