Suppose that $\mathcal{G}$ is etale principal groupoid and that $G$ is a discrete (or finite) group acting freely on the locally compact unit space $\mathcal{G}^0$ (or assuming compactness, if necessary). Then there is induced action of $G$ on $\mathcal{G}$ and we can form the semidirect product groupoid $\mathcal{G} \rtimes G$.
Will $\mathcal{G} \rtimes G$ ever be principal or essentially principal groupoid?
Edit: I believe that for $\mathcal{G} \rtimes G$ to be principal, we must have that for every $g \in G$ there is no $\gamma \in \mathcal{G}$ with the $r(\gamma) = s(\gamma).g$, but I am less certain about what might imply essentially principal.
The relevant terminology, is I am using Renault's book "A groupoid approach to C*-algebras".
