Simplicity of the C*-algebras of skew product k-graphs

We consider conditions on a $k$-graph $\Lambda$, a semigroup $S$ and a functor $\eta : \Lambda \to S$ which ensure that the $C^*$-algebra of the skew-product graph $\Lambda \times_\eta S$ is simple. Our results allow give some necessary and sufficient conditions for the AF-core of a $k$-graph $C^{*}$-algebra to be simple.