Lemma 76.15.3. Let $B \to S$ as in Section 76.3. Let $(U, R, s, t, c)$ be a groupoid in algebraic spaces over $B$, and let $G/U$ be its stabilizer. Denote $R_ t/U$ the algebraic space $R$ seen as an algebraic space over $U$ via the morphism $t : R \to U$. There is a canonical left action
induced by the composition law $c$.