Abstract
The project investigates symmetries of Lie groupoids up to Morita equivalence, providing a good notion of symmetries in the setting of differentiable stacks. We pay special attention to two different problems, namely, the Marsden-Weinstein reduction of Hamiltonian actions of Lie 2-groups on pre-symplectic Lie groupoids and the equivariant cohomology of a Lie 2-group action on a Lie groupo…