Exact Sequence of $0$-Order Pseudodifferential Operators on a Lie Groupoid

Associated to a Lie groupoid, there are two $C^{\ast }$-algebras: the full and the reduced one. The associated order $0$ pseudodifferential calculus gives rise to multiplier algebras of both. We prove that both associated corona algebras are equal to the natural (commutative) principal symbol algebras.