From the introduction: The result of the present paper is a Lefschetz formula for manifolds with conical singularities. The elliptic theory for such manifolds is well developed. So it is natural to ask for a Lefschetz number in this situation.
Let us indicate the main feature of our theory. The Lefschetz number is given by a sum of contributions from the interior part of the manifold (which has the standard Atiyah-Bott form) and from the singular points. The latter ones are expressed in terms of analytic families, namely, the conormal symbols of the operators in the complex and the conormal symbols of the operators constituting the endomorphism.