Quantum Steenrod squares and the equivariant pair-of-pants in symplectic cohomology

We relate the quantum Steenrod square to Seidel’s equivariant pair-of-pants product for open convex symplectic manifolds that are either monotone or exact, using an equivariant version of the PSS isomorphism. We proceed similarly for $\mathbb{Z}\mathrm{/}2$-equivariant symplectic cohomology, using an equivariant version of the continuation and $c^{\ast }$-maps. We prove a symplectic Cartan relation, pointing out the difficulties in stating it. We give a nonvanishing result for the equivariant pair-of-pants product for some elements of $S{H}^{\ast }(T^{\ast }{S}^n)$. We finish by calculating the symplectic square for the negative line bundles $M = $\text{Tot}$($\mathcal{O}$(-1) \rightarrow $\mathbb{C}\mathbb{P}$^m)$, proving an equivariant version of a result due to Ritter.