2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62824An action of ${\mathbb Z}^k$ is associated to a higher rank graph $Λ$ satisfying a mild assumption. This generalises the construction of a topological Markov shift arising from a nonnegative 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.Sixteen pages with no figures. To appear Ergodic Theory and Dynamical SystemsOperator Algebras46L05; 46L55text