On (Z2)k actions

Suppose that (Mm,Φ) is a smooth (Z2)k action on a closed smooth m-dimensional manifold whose fixed point set is a connected n-dimensional submanifold Fn. In this paper we prove that: (a) t;2kn, (Mm,Φ) bounds equivariantly; kn, (Mm,Φ) is equivariantly cobordant to the twist on Fn×⋯×Fn (2k times). uestion was posed by C. Kosniowski and R.E. Stong twenty years ago, after they proved it for k=1.