Consider the groupoid $Vect_n(S)$ of rank n-vector bundles over a projective surface $S$. What does it mean to have a sheaf $$\mathcal L\in QCoh(Vect_n(S))?$$ A notion of quasicoherent sheaf on a groupoid should be involved, but I guess that the groupoid should have "some topology".
Sorry for the vagueness of the question, but I have been spoken about this and I realise I don't quite understand the notion.
Thank you in advance.
$\text{Vect}_n(S)$ is a stack, not a groupoid. Its functor of points sends a commutative ring $R$ to the groupoid of rank $n$ vector bundles on $S \times \text{Spec } R$. $L$ is a quasicoherent sheaf on this stack.