  We study the stable category of the factor algebra of the preprojective
algebra associated with an element $w$ of the Coxeter group of a quiver. We
show that there exists a silting object $M(\bf{w})$ of this category associated
with each reduced expression $\bf{w}$ of $w$ and give a sufficient condition on
$\bf{w}$ such that $M(\bf{w})$ is a tilting object. In particular, the stable
category is triangle equivalent to the derived category of the endomorphism
algebra of $M(\bf{w})$. Moreover, we compare it with a triangle equivalence
given by Amiot-Reiten-Todorov for a cluster category.

Representation Theory