We construct products on the homology of quotients by finite group actions of the free loop space ΛM of a compact manifold M. We compute some of the these products in the case M is as sphere. We show that there are nonnilpotent classes with respect to these products for spheres. The energy functional on ΛM associated to a Riemannian metric on M is invariant under the group actions we consider. We therefore retain information about geometrically distinct closed geodesics.