  We introduce group actions on polyfolds and polyfold bundles. We prove
quotient theorems for polyfolds, when the group action has finite isotropy. We
prove that the sc-Fredholm property is preserved under quotient if the base
polyfold is infinite dimensional. The quotient construction is the main
technical tool in the construction of equivariant fundamental class in [42]. We
also analyze the equivariant transversality near the fixed locus in the
polyfold setting. In the case of $S^1$-action with fixed locus, we give a
sufficient condition for the existence of equivariant transverse perturbations.
We outline the application to Hamiltonian-Floer cohomology and a proof of the
weak Arnold conjecture for general symplectic manifolds, assuming the existence
of Hamiltonian-Floer cohomology polyfolds.
