-actions fixing KdPs2∪KdPeven

The main result of this paper is the determination, up to equivariant cobordism, of all manifolds with -action whose fixed point set is F=KdPs2∪KdPn, where n⩾2s+1 is even and s⩾1. Here, KdPn is the real (d=1), complex (d=2) or quaternionic (d=4) n-dimensional projective space, with real dimension dn. This extends a previous and recent result of the authors, concerning the case d=1 and s=1. We also obtain this equivariant cobordism classification for d=2 and 4 in the cases F={point}∪KdPn, where n⩾2 is even, and F=KdPm∪KdPn, where m is odd and n⩾0 is even; for d=1 and k=1, these results are due to D.C. Royster.