Some computations in equivariant cobordism in relation to Milnor manifolds

Let N⁎ be the unoriented cobordism algebra, let G=(Z2)n and let Z⁎(G) denote the equivariant cobordism algebra of G-manifolds with finite stationary point sets. Let ϵ⁎:Z⁎(G)→N⁎ be the homomorphism which forgets the G-action. We use Milnor manifolds (degree 1 hypersurfaces in RPm×RPn) to construct non-trivial elements in Z⁎(G). We prove that these elements give rise to indecomposable elements in Z⁎(G) in degrees up to 2n−5. Moreover, in most cases these elements can be arranged to be in Ker(ϵ⁎).