  Given an algebra and a finite group acting on it via automorphisms, a natural
object of study is the associated skew group algebra. In this article, we study
the relationship between quasi-hereditary structures on the original algebra
and on the corresponding skew group algebra. Assuming a natural compatibility
condition on the partial order, we show that the skew group algebra is
quasi-hereditary if and only if the original algebra is. Moreover, we show that
in this setting an exact Borel subalgebra of the original algebra which is
invariant as a set under the group action gives rise to an exact Borel
subalgebra of the skew group algebra, and that under this construction,
properties such as normality and regularity of the exact Borel subalgebra are
preserved.
