Adiabatic groupoid, crossed product by ${\mathbb{R}}_{+}^{\ast }$ and Pseudodifferential calculus

Claire Debord, Georges Skandalis

We consider the crossed product $G_{ga}$ by ${\mathbb{R}}_{+}^{\ast }$ of the adiabatic groupoid associated with any Lie groupoid $G$. We construct an explicit Morita equivalence between the exact s…