  By restricting to a class of localic open groupoids $G$ which, similarly to
Lie groupoids, possess appropriate covers $\widehat G\to G$ by \'etale
groupoids, we extend results about groupoid actions and quantales that were
previously proved for \'etale groupoids but do not seem to work for arbitrary
open groupoids. In particular we obtain a characterization of the category of
$G$-actions as a category of quantale modules on $\mathcal O(\widehat G)$ that
satisfy a condition related to the quantale $\mathcal O(G)$. This leads to a
simple description of $G$-sheaves and the classifying topos of $G$ in terms of
Hilbert $\mathcal O(\widehat G)$-modules. The bicategory whose 1-cells are the
groupoid bi-actions is bi-equivalent to a corresponding bicategory of quantales
and bimodules.
