  We construct a noncommutative desingularization of the discriminant of a
finite reflection group $G$ as a quotient of the skew group ring $A=S*G$. If
$G$ is generated by order two reflections, then this quotient identifies with
the endomorphism ring of the reflection arrangement $\mathcal{A}(G)$ viewed as
a module over the coordinate ring $S^G/(\Delta)$ of the discriminant of $G$.
This yields, in particular, a correspondence between the nontrivial irreducible
representations of $G$ to certain maximal Cohen--Macaulay modules over the
coordinate ring $S^G/(\Delta)$. These maximal Cohen--Macaulay modules are
precisely the nonisomorphic direct summands of the coordinate ring of the
reflection arrangement $\mathcal{A} (G)$ viewed as a module over
$S^G/(\Delta)$. We identify some of the corresponding matrix factorizations,
namely the so-called logarithmic (co-)residues of the discriminant.
