For a domestic finite group scheme, we give a direct description of the Euclidean components in its Auslander-Reiten quiver via the McKayquiver of a finite linearly reductive subgroup scheme of SL(2). Moreover, for a normal subgroup scheme N of a finite group scheme G, we show that there is a connection between the ramification indices of the restriction morphism P(VN ) → P(VG) between their projectivized cohomological support varieties and the ranks of the tubes in their Auslander-Reiten quivers.

We investigate the representation theory of domestic group schemes 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 kG.