  In this paper, we study genuine equivariant factorization homology and its
interaction with equivariant Thom spectra, which we construct using the
language of parametrized higher category theory. We describe the genuine
equivariant factorization homology of Thom spectra, and use this description to
compute several examples of interest. A key ingredient for our computations is
an equivariant nonabelian Poincar\'e duality theorem, in which we prove that
factorization homology with coefficients in a $G$-space is given by a mapping
space. We compute the Real topological Hochschild homology ($THR$) of the Real
bordism spectrum $MU_\mathbb{R}$ and of the equivariant Eilenberg--MacLane
spectra $H\underline{\mathbb{F}}_2$ and $H\underline{\mathbb{Z}}_{(2)}$, as
well as factorization homology of the sphere $S^{2\sigma}$ with coefficients in
these Eilenberg--MacLane spectra. In Appendix B, Jeremy Hahn and Dylan Wilson
compute $THR(H\underline{\mathbb{Z}})$.
