On the homotopy classification of elliptic operators on stratified   manifolds
  We find the stable homotopy classification of elliptic operators on stratified manifolds. Namely, we establish an isomorphism of the set of elliptic operators modulo stable homotopy and the $K$-homology group of the singular manifold. As a corollary, we obtain an explicit formula for the obstruction of Atiyah--Bott type to making interior elliptic operators Fredholm. 
V. E. Nazaikinskii, A. Yu. Savin, and B. Yu. Sternin