$\mathrm{\infty }$-categorical group quotients via skew group algebras

We relate group quotients of dg-categories and linear stable $\mathrm{\infty }$-categories. Given a group acting on a dg-algebra, we prove that the skew group dg-algebra is Morita equivalent to the dg-categorical homotopy group quotient. We also treat the cases of group actions on dg-categories, with corresponding skew group dg-categories, and of orbit dg-categories. Finally, we describe a version of the skew group algebra in the setting of ring spectra and relate it with $\mathrm{\infty }$-categorical group quotients.