  In this paper we study representations of skew group algebras $\Lambda G$,
where $\Lambda$ is a connected, basic, finite-dimensional algebra (or a locally
finite graded algebra) over an algebraically closed field $k$ with
characteristic $p \geqslant 0$, and $G$ is an arbitrary finite group each
element of which acts as an algebra automorphism on $\Lambda$. We characterize
skew group algebras with finite global dimension or finite representation type,
and classify the representation types of transporter categories for $p \neq
2,3$. When $\Lambda$ is a locally finite graded algebra and the action of $G$
on $\Lambda$ preserves grading, we show that $\Lambda G$ is a generalized
Koszul algebra if and only if so is $\Lambda$.
