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In this paper we compute homotopical equivariant bordism for the group Z/2, namely MO Z/2 * , geometric equivariant bordism n Z/2 * , and their quotient as modules over geometric bordism. This quotient is a module of stable transversality obstructions. We construct these rings from knowledge of their localizations.

Real equivariant bordism and stable transversality obstructions for $\mathbb {Z}/2$