Galois actions and blocks of tame infinitesimal group schemes

Given an infinitesimal group G, that is defined over an algebraically closed field of characteristic p >= 3, we determine the block structure of the algebra of measures H( G) in case its principal block B(0)(G) is tame and the height of the factor group G/M(G) of G by its multiplicative center M( G) is at least two. Our results yield a complete description of the stable Auslander-Reiten quiver of H( G) along with a criterion for the domesticity of H( G).