  It is shown that, the quasi-Koszulities of algebras and modules are Morita
invariance. A finite-dimensional $K$-algebra $A$ with an action of $G$ is
quasi-Koszul if and only if so is the skew group algebra $A \ast G$, where $G$
is a finite group satisfying $\char K \nmid |G|$. A finite-dimensional
$G$-graded $K$-algebra $A$ is quasi-Koszul if and only if so is the smash
product $A # G^*$, where $G$ is a finite group satisfying $\char K \nmid |G|$.
These results are applied to prove that, if a finite-dimensional connected
quiver algebra is Koszul then so are its Galois covering algebras with finite
Galois group $G$ satisfying $\char K \nmid |G|$. So one can construct Koszul
algebras by finite Galois covering. Moreover, a general construction of Koszul
algebras by Galois covering with finite cyclic Galois group is provided. As
examples, many Koszul algebras are constructed from exterior algebras and
Koszul preprojective algebras by finite Galois covering with either cyclic or
noncyclic Galois group.
