The mackey machine for crossed products by regular groupoids. I

We first describe a Rieffel induction system for groupoid crossed products. We then use this induction system to show that, given a regular groupoid G and a dynamical system (A, G, α), every irreducible representation of A ⋊ G is induced from a representation of the group crossed product A(u) ⋊ S_u where u ε G⁽⁰⁾, A(u) is a fibre of A, and S_u is a stabilizer subgroup of G.