  We study the gerbal representations of a finite group $G$ or, equivalently,
module categories over Ostrik's category $Vec_G^\alpha$ for a 3-cocycle
$\alpha$. We adapt Bartlett's string diagram formalism to this situation to
prove that the categorical character of a gerbal representation is a module
over the twisted Drinfeld double $D^\alpha(G)$. We interpret this twisted
Drinfeld double in terms of the inertia groupoid of a categorical group.
