  We investigate the representation theory of domestic group schemes
$\mathcal{G}$ over an algebraically closed field of characteristic $p > 2$. We
present results about filtrations of induced modules, actions on support
varieties, Clifford theory for certain group schemes and applications of
Clifford theory for strongly group graded algebras to the structure of
Auslander-Reiten quivers. The combination of these results leads to the
classification of modules belonging to the principal blocks of the group
algebra $k\mathcal{G}$.
