over a ring $R$ is denoted by $(\mathbf{FGSch}/R)$.

(3) Let $G$ be a flat group scheme over the noetherian ring $R$. When dealing with representations of $G$ we follow the conventions of [@jantzen87 Part I, Ch. 2] with the exception that the word “representation” is reserved for $G$-modules which are of finite type over $R$. The category of representations is denoted by ${{\mathrm{Rep}}_{R}(G)}$. The full subcategory of representations which underlie locally free $R$-modules is denoted by ${\rm Rep}_R^\circ(G)$.

(4) The [*right-regular*]{}, respectively [*left-regular*]{}, $G$-module [@jantzen87 2.7] shall be denoted by $R[G]_{\rm right}$, respectively $R[G]_{\rm left}$.

(5) If $f:G\to H$ is an arrow of $({\mathbf{FGSch}}/R)$, we let $f^\#:{{\mathrm{Rep}}_{R}(H)}\to{{\mathrm{Rep}}_{R}(G)}$ be the restriction functor.

 On torsors  {#on-torsors .unnumbered}
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(1) Let $R$ be a ring, $X$ an $R$-scheme, $G$ and $H$ group schemes over $R$, $P
    \to X$ a $G$-torsor and $Q\to X$ an $H$-torsor. A [*generalized morphism*]{} from $P$ to $Q$ is a couple $(f,\rho)$ consisting of an arrow of $X$-schemes $f:P\to Q$ and a morphism of group schemes $\rho:G\to H$ such that, for points with value on arbitrary $R$-algebras, we have $f(yg)=f(y)\rho(g)$. In this case, we say that the generalized morphism [*covers*]{} the morphism $\rho$. If $G=H$, then a morphism of 