  Inspired by the recent experimental observation of strongly coupled
polaritons in a Moir\'e heterobilayer, we study a model of dipole-interacting
excitons localized on sites of a lattice and coupled to planar cavity photons.
We calculate the phase diagram of this system by computing fluctuations around
the mean field and determining the stability of the excitation spectrum. We
find that the transition from the normal state to a polariton condensate is
intermediated by a series of ordered states at partial fillings of the exciton
lattice, stabilized by the exciton interactions. In particular we predict a
supersolid phase in which a polariton condensate coexists with spatial order.
