Lemma 39.17.5. Let $S$ be a scheme. Let $(U, R, s, t, c)$ be a groupoid scheme over $S$. Let $p \in U \times _ S U$ be a point. Denote $R_ p$ the scheme theoretic fibre of $j = (t, s) : R \to U \times _ S U$. If $R_ p \not= \emptyset $, then the action

(see Lemma 39.17.4) which turns $R_ p$ into a $G_{\kappa (p)}$-torsor over $\kappa (p)$.

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