  Let $\cal A$ be a maximal (or more generally a hereditary) order in a central
simple algebra over a global field $F$ of positive characteristic. We study the
reduction of the modular scheme of $\cal A$-elliptic sheaves at all places of
$F$. We show that some of these varieties - for different $\cal A$ - are twists
of each other. This result can be viewed as a global analogue of the
Cherednik-Drinfeld theorem for these varieties.
