Elliptic Theory on Manifolds with Corners: II. Homotopy classification   and $K$-Homology
  We establish the stable homotopy classification of elliptic pseudodifferential operators on manifolds with corners and show that the set of elliptic operators modulo stable homotopy is isomorphic to the K-homology group of some stratified manifold. By way of application, generalizations of some recent results due to Monthubert and Nistor are given. 
V. E. Nazaikinskii, A. Yu. Savin, and B. Yu. Sternin