Actions of semigroups on directed graphs and their C*-algebras

A free action a of a group C on a row-finite directed graph E induces an ac tion a, on its Cuntz-Krieger C*-algebra C*(E), and a recent theorem of Kumj ian and Pask says that the crossed product C*(E) X-x* G is stably isomorphi c to the C*-algebra C*(E/G) of the quotient graph. We prove an analogue for free actions of Ore semigroups. The main ingredients are a new generalisat ion of a theorem of Gross and Tucker, dilation theory for endomorphic actio ns of Ore semigroups on graphs and C*-algebras, and the Kumjian-Pask Theore m itself. (C) 2001 Elsevier Science B.V. All rights reserved.