C*-algebras of directed graphs and group actions

Given a free action of a group G on a directed graph E we show that the cro ssed product of C*(E), the universal C*-algebra of E, by the induced action is strongly Morita equivalent to C*(E/G). Since every connected graph E ma y be expressed as the quotient of a tree T by an action of a free group G w e may use our results to show that C*(E) is strongly Morita equivalent to t he crossed product C-0(partial derivative T) x G, where partial derivative T is a certain zero-dimensional space canonically associated to the tree.