  The main theorem describes the behaviour of the stable cohomotopy invariant
defined in the first article (joint with M. Furuta) in this series of two under
the operation of taking connected sums of four-manifolds: The invariant of a
connected sum is the smash product (in the sense of equivariant spectra) of the
invariants of the respective summands. This provides nonvanishing results even
in cases in which both the integer valued Seiberg-Witten invariants and
Donaldson invariants have to vanish. As a consequence, one gets new results on
diffeomorphism types of decomposable four-manifolds.
