Equivariant bordisms

The article investigates the category of manifolds acted upon by a Lie group $G$ in such a way that the orbit of every point is equivariantly diffeomorphic to one of a fixed set $S$ of homogeneous spaces of $G$. The bordism groups ($S$-equivariant bordism groups) are defined in a natural way. These groups are described in detail in the special cases of the quasicomplex action of the groups $U(1)$ and $SU(2)$ on quasicomplex manifolds.