Geodesic
Equivariant bordisms
Matematičeskie zametki, Tome 10 (1971) no. 5, pp. 519-526.

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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. 
@article{MZM_1971_10_5_a4,
     author = {A. M. Karminskii},
     title = {Equivariant bordisms},
     journal = {Matemati\v{c}eskie zametki},
     pages = {519--526},
     publisher = {mathdoc},
     volume = {10},
     number = {5},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_5_a4/}
}
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A. M. Karminskii. Equivariant bordisms. Matematičeskie zametki, Tome 10 (1971) no. 5, pp. 519-526. http://geodesic.mathdoc.fr/item/MZM_1971_10_5_a4/