Group actions on topological graphs

We define the action of a locally compact group G on a topological graph E. This action induces a natural action of G on the C ^*- correspondence H(E) and on the graph C ^*-algebra C ^*(E). If the action is free and proper, we prove that C ^*(E)×r G is strongly Morita equivalent to C ^*(E/G). We define the skew product of a locally compact group G by a topological graph E via a cocycle c:E ¹ → G. The group acts freely and properly on this new topological graph EA - c G. If G is abelian, there is a dual action on C ^* (E) such that $C*(E) {G}\cong C*(E×cG)$. We also define the fundamental group and the universal covering of a topological graph.