  The Floer cohomology of a symplectic automorphism and that of its square are
related by the pair-of-pants product. For exact symplectic automorphisms, we
introduce an equivariant version of that product, and use it to prove a
Smith-type inequality of ranks between Floer cohomology groups. Under
additional topological assumptions, the same inequality was previously proved
by Hendricks, using a different strategy.
