  The paper is based on a talk. Complete exposition is given in "Equivariant
Hirzebruch class for singular varieties".
  Starting from the classical theory we describe Hirzebruch class and the
related Todd genus of a complex singular algebraic varieties. When the variety
is equipped with an action of an algebraic torus we localize the Hirzebruch
class at the fixed points of the action. We give some examples of computations.
