On rigid Hirzebruch genera

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 stably complex manifolds. In particular, we are proving that a genus is rigid if and only if it is a generalized Todd genus.