Oriented orbifold cobordism with rational coefficients is fairly well understood-invariants and generators are known. One step in studying the actual orbifold cobordism ring involves determining which combinations of finite, degree n subgroups of SO(n) can occur in an oriented or locally oriented n dimensional orbifold. This was key in calculations up through dimension four.

I'll give a brief overview of orbifold cobordism with examples and pictures. I'll then focus on the above question by providing a first obstruction to a given set of such subgroups occurring in some oriented n-orbifold. This is the only obstruction in dimensions two through four. From this we build a differential d associated with finite degree n subgroups of SO(n), with n varying, and hence obtain a homology.

I'll show how this homology relates to orbifold cobordism and compute d for many cases, including dimensions less than or equal to four and also direct sums and products. Additionally, if an oriented degree n group G admits an orientation reversing linear automorphism u, we construct a semidirect product of G by (u,-1) in degree n+1. I'll present equations for calculating d of this semidirect product.