  The classical multiplicative (Hirzebruch) genera of manifolds have the
wonderful property which is called rigidity. Rigidity of a genus h means that
if a compact connected Lie group G acts on a manifold X, then the equivariant
genus h^G(X) is independent on G, i.e. h^G(X)=h(X). In this paper we are
considering the rigidity problem for complex manifolds. In particular, we are
proving that a genus is rigid if and only if it is a generalized Todd genus.
