Actions of Zᵏ associated to higher rank graphs

An action of Zᵏ is associated to a higher rank graph Λ satisfying a mild assumption. This generalizes the construction of a topological Markov shift arising from a non-negative integer matrix. We show that the stable Ruelle algebra of Λ is strongly Morita equivalent to C^*(Λ) . Hence, if Λ satisfies the aperiodicity condition, the stable Ruelle algebra is simple, stable and purely infinite.