  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.
