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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 our future work. 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.

Quotient theorems in polyfold theory and S 1 ‐equivariant transversality