  A global action is the algebraic analogue of a topological manifold. This
construction was introduced in first place by A. Bak as a combinatorial
approach to K-Theory and the concept was later generalized by Bak, Brown,
Minian and Porter to the notion of groupoid atlas. In this paper we define and
investigate homotopy invariants of global actions and groupoid atlases, such as
the strong fundamental groupoid, the weak and strong nerves, classifying spaces
and homology groups. We relate all these new invariants to classical
constructions in topological spaces, simplicial complexes and simplicial sets.
This way we obtain new combinatorial formulations of classical and non
classical results in terms of groupoid atlases.
