We consider a free action of an Ore semigroup on a higher-rank graph, and the induced action by endomorphisms of the C ∗-algebra of the graph. We show that the crossed product by this action is stably isomorphic to the C ∗-algebra of a quotient graph. Our main tool is Laca’s dilation theory for endomorphic actions of Ore semigroups on C ∗-algebras, which embeds such an action in an automorphic action of the enveloping group on a larger C ∗-algebra.
Maloney, B., Pask, D. & Raeburn, I. (2014). Skew-products of higher-rank graphs and crossed products by semigroups. Semigroup Forum, 88 (1), 162-176.