Abstract
Let A be the family of all equivariant bordism classes of involutions containing a representative ( M, T) with M connected and with the fixed point set of T being the disjoint union of a fixed connected n-dimensional manifold V n and a point. In this paper we analyse the influence of A in the determination of the equivariant bordism classes of ( Z 2) κ-actions which contain a representative fixing V n ∪ point. The results obtained are used to determine, up to bordism, all possible ( Z 2) κ-actions fixing RP(n) ∪ point with n odd.
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