We construct model category structures on various types of (marked) *-categories. These structures are used to present the infinity categories of (marked) *-categories obtained by inverting (marked) unitary equivalences. We use this presentation to explicitly calculate the $\infty$-categorical G-fixed points and G-orbits for G-equivariant (marked) *-categories.
Keywords: *-categories, model categories, $\infty$-categories, limits and colimits
2010 MSC: 18C35,55U35
Theory and Applications of Categories, Vol. 34, 2019, No. 27, pp 781-853.