Symmetric group actions on homotopy S2 x S2

Let X be a closed smooth 4-manifold which is homotopy equivalent to S-2 x S-2. In this paper we use Seiberg-Witten theory to prove that if X admits a spin symmetric group S-4 action of even type with b(2)(+) (X/S-4) = b(2)(+)(X), then as an element of R(S-4), Ind D-S4 (X) = k(1)(1 - theta) + k(2)(psi(1) - psi(2)) for some integers k(1) and k(2), where 1, theta, psi(1), psi(2) are irreducible characters of S-4 of degree 1, 1, 3, and 3 respectively.