The integral homology of Coxeter cellular complexes

We define a special q-CW complex, named Coxeter cellular complex, and give an explicit boundary map which can reflect the information of local groups. The orbifold homology groups we defined have some similar properties as usual cellular homology theory, such as Hurewize Theorem. Moreover, I will compute the homology groups of Coxeter orbifolds and some (non-Coxeter) orbifolds in this talk. This is a joint work with Professor Zhi Lü and Li Yu.