Almost complex structure, blowdowns and McKay correspondence in quasitoric orbifolds

We prove the existence of invariant almost complex structure on any positively omnioriented quasitoric orbifold. We construct blowdowns. We define Chen-Ruan cohomology ring for any omnioriented quasitoric orbifold. We prove that the Euler characteristic of this cohomology is preserved by a crepant blowdown. We prove that the Betti numbers are also preserved if dimension is less or equal to six. In particular, our work reveals a new form of McKay correspondence for orbifold toric varieties that are not Gorenstein. We illustrate with an example.