  The graph C*-algebra of a directed graph E is the universal C*-algebra
generated by a family of partial isometries satisfying relations which reflect
the path structure of E. In the first part of this paper we consider coverings
of directed graphs: morphisms p:F->E which are local isomorphisms. We show that
the graph algebra C*(F) can be recovered from C*(E) as a crossed product by a
coaction of a homogeneous space associated to the fundamental group \pi_1 (E).
These crossed products provide a good model for a general theory of crossed
products by homogeneous spaces. The second part of the paper is devoted to
building a framework for studying crossed products by homogeneous spaces using
Rieffel's theory of proper actions.
