Finiteness properties and homological dimensions of skew group rings

Let [Formula: see text] be a finite group acting on a ring [Formula: see text] and [Formula: see text] a subgroup of [Formula: see text]. In this paper, we compare some homological dimensions over the skew group rings [Formula: see text] and [Formula: see text]. Moreover, under the assumption that [Formula: see text] is a separable extension over [Formula: see text], we show that the skew group rings [Formula: see text] and [Formula: see text] share some properties such as being [Formula: see text]-Gorenstein, [Formula: see text]-perfect, [Formula: see text]-coherent, [Formula: see text], Ding–Chen or IF-rings.