Finite Group Actions on Spin Bundles

Let L be a complex line bundle over a closed, oriented, smooth 4-manifold X with c1(L) ≡ w2(TX) mod 2. Let a finite group G act on X as orientation preserving isometries and on L such that the projection L → X is a G-map. We investigate the action of G on the Seiberg-Witten equations, and when G = Z2 we study the G-invariant Seiberg-Witten invariants on X and the Seiberg-Witten invariants on its quotient setting.