Involutions fixing , I

This paper studies the equivariant cobordism classification of all involutions fixing a disjoint union of an odd-dimensional real projective space with its normal bundle nonbounding and a Dold manifold with and . For odd , the complete analysis of the equivariant cobordism classes of such involutions is given except that the upper and lower bounds on codimension of may not be best possible; for even , the problem may be reduced to the problem for even projective spaces.