  We study the geometry of the stratification induced by an affine hyperplane
arrangement H on the quotient of a complex affine space by the action of a
discrete group preserving H. We give conditions ensuring normality or normality
in codimension 1 of strata. As an application, we provide the list of those
categorical quotients of closures of Jordan classes and of sheets in all
complex simple algebraic groups that are normal. In the simply connected case,
we show that normality of such a quotient is equivalent to its smoothness.
