  Tilting objects play a key role in the study of triangulated categories. A
famous result due to Iyama and Takahashi asserts that the stable categories of
graded maximal Cohen-Macaulay modules over quotient singularities have tilting
objects. This paper proves a noncommutative generalization of Iyama and
Takahashi's theorem using noncommutative algebraic geometry. Namely, if $S$ is
a noetherian AS-regular Koszul algebra and $G$ is a finite group acting on $S$
such that $S^G$ is a "Gorenstein isolated singularity", then the stable
category ${\underline {\operatorname {CM}}}^{\Bbb Z}(S^G)$ of graded maximal
Cohen-Macaulay modules has a tilting object. In particular, the category
${\underline {\operatorname {CM}}}^{\Bbb Z}(S^G)$ is triangle equivalent to the
derived category of a finite dimensional algebra.
