A Continuous Field of C*-algebras and the Tangent Groupoid for Manifolds   with Boundary
  For a smooth manifold with boundary we construct a semigroupoid and a continuous field of C*-algebras which extend Connes' construction of the tangent groupoid.   We show the asymptotic multiplicativity of \hbar-scaled truncated pseudodifferential operators with smoothing symbols and compute the K-theory of the associated symbol algebra. 
Johannes Aastrup, Ryszard Nest and Elmar Schrohe