continuous field of C∗-algebras and the tangent groupoid for manifolds with boundary

For a smooth manifold X with boundary we construct a semi-groupoid T −X and a continuous field C∗r (T −X) of C∗-algebras which extend Connes’ construction of the tangent groupoid. We show the asymptotic multiplicativity of ¯h-scaled truncated pseudodifferential operators with smoothing symbols and compute the K-theory of the associated symbol algebra. © 2005 Elsevier Inc. All rights reserved.