Cohomology of toroidal orbifold quotients

Let φ:Z/p→GLn(Z) denote an integral representation of the cyclic group of prime order p. This induces a Z/p-action on the torus X=Rn/Zn. The goal of this paper is to explicitly compute the cohomology groups H⁎(X/Z/p;Z) for any such representation. As a consequence we obtain an explicit calculation of the integral cohomology of the classifying space associated to the family of finite subgroups for any crystallographic group Γ=Zn⋊Z/p with prime holonomy.