Actions of Z^k associated to higher rank graphs

We construct an action of $\mathbb Z^k$ on a compact zero-dimensional space obtained from a higher graph $\Lambda$ satisfying a mild assumption generalizing the construction of the Markov shift associated to a nonnegative integer matrix. The stable Ruelle algebra $R_s(\Lambda)$ is shown to be strongly Morita equivalent to $C^*(\Lambda)$. Hence $R_s(\Lambda)$ is simple, stable and purely infinite, if $\Lambda$ satisfies the aperiodicity condition.