G-bordism with singularities and G-homology (Q1067649)

In consequence of the study of ordinary G-homology and cohomology theories to be represented by the bordism and cobordism theories of singular G-manifolds, the main results the authors obtain are as follows. 1. The Bredon-Illman cohomology theory, together with its RO(G)-graded extension, is represented as singular RO(G)-graded cobordism. 2. The cohomology theory \(H^*(X\times_ G EG; {\mathbb{Z}})\), viewed as a cohomology theory on X, is represented by ''stable tom Dieck cobordism with sigularities'' of codimension 2. 3. The above singular theories are related via inversion of a canonical Chern class in the RO(G) theory.