Zk2-actions fixing kdp2s U kdp even

The main result of this paper is the determination, up to equivariant cobordism, of all manifolds with Z 2 k -action whose fixed point set is F = K d P 2 s ∪ K d P n , where n ⩾ 2 s + 1 is even and s ⩾ 1 . Here, K d P n 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 } ∪ K d P n , where n ⩾ 2 is even, and F = K d P m ∪ K d P n , where m is odd and n ⩾ 0 is even; for d = 1 and k = 1 , these results are due to D.C. Royster.