In a joint work with A. Cabrera (UFRJ) and E. Pujals (IMPA) we study actions of discrete groups over connected manifolds by means of their orbit stacks. Stacks are categorified spaces, they generalize manifolds and orbifolds, and they remember the isotropies of the actions that give rise to them. I will review the basics, show that for simply connected spaces the stacks recover the dynamics up to conjugacy, and discuss the general case. I will also discuss several examples, involving irrational rotations of the circle, hyperbolic toral automorphisms, and the lens spaces.