  We prove that given a regular groupoid $G$ whose isotropy subgroupoid $S$ has
a Haar system, along with a dynamical system $(A,G,\alpha)$, there is an action
of $G$ on the spectrum of $A\rtimes S$ such that the spectrum of $A\rtimes G$
is homeomorphic to the orbit space of this action via induction. In addition,
we give a strengthening of these results in the case where the crossed product
is a groupoid algebra.
