  We study rotating quasi-two-dimensional Bose-Einstein-condensates, in which
atoms are dressed to a highly excited Rydberg state. This leads to weak
effective interactions that induce a transition to a mesoscopic supersolid
state. Considering slow rotation, we determine its superfluidity using Quantum
Monte-Carlo simulations as well as mean field calculations. For rapid rotation,
the latter reveal an interesting competition between the supersolid crystal
structure and the rotation-induced vortex lattice that gives rise to new
phases, including arrays of mesoscopic vortex crystals.
