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A polyhedral product is a natural subspace of a Cartesian product, which isspecified by a simplicial complex K. The automorphism group Aut(K) of K inducesa group action on the polyhedral product. In this paper we study this groupaction and give a formula for the fixed point set of the polyhedral product forany subgroup H of Aut(K). We use the fixed point data to compute examples ofBredon cohomolohgy for small non-Abelian groups such as $D_8$ and $\Sigma_4$.

Bredon Cohomology of Polyhedral Products