Equivariant RO(G)-graded bordism theories

Let G be a finite group. The RO(G)-graded bordism theories of Pulikowski 7] and Kosniowski 3] are studied. Representing equivariant Thom spectra are constructed, and the relevant transversality results proved. New methods for splitting away from the order of G are described, and behavior in the presence of a gap hypothesis is examined.