  For a finite acyclic quiver $Q$ and the corresponding preprojective algebra
$\Pi$, we study the factor algebra $\Pi_w$ associated with a element $w$ in the
Coxeter group introduced by Buan-Iyama-Reiten-Scott. The algebra $\Pi_w$ has a
natural $\mathbb{Z}$-grading, and we prove that
$\underline{\mathsf{Sub}}^{\mathbb{Z}}\Pi_w$ has a tilting object $M$.
Moreover, we show that the endomorphism algebra of $M$ is isomorphic to the
stable Auslander algebra of a certain torsion free class of $\mathsf{mod}\,kQ$.
