Discrete Group Actions and Generalized Real Bott Manifolds

We study a class of discrete group actions on the Euclidean space.In particular, we will investigate when the orbit spaces of such group actions are closed manifolds.The answer turns out to be a class of real toric manifolds called generalized real Bott manifolds which are the total spaces of some kind of iterated real projective space bundles.This relation provides a new viewpoint on generalized real Bott manifolds which might be useful for the future study.