0_3397 Dipolar excitons of bilayer heterostructures provide unique opportunities to experimentally explore collective phases accessible to strongly correlated bosonic systems. In fact, by enforcing a spatial separation between electrons and holes constituting dipolar excitons, one imprints a permanent gigantic electric dipole, yielding strong quasi-long-range dipolar repulsions between excitons.Here, we report studies emphasising dipolar excitons of GaAs bilayers. We manipulate the interaction between the excitons dipole and a gate defined electric field to confine dipolar excitons in 200 to 500 nm period  lattice potentials. Then, we evidence that on-site repulsive dipolar interactions stabilise Mott insulating phases at sub-Kevin temperatures, with either one or two excitons uniformly filling up to 100 lattice sites. For sufficiently small lattice periods, we further show that dipolar excitons allow for the first implementation of the Bose-Hubbard model extended by nearest neighbour interactions, so that an insulating phase is stabilised at half-filling, excitons thus realising a checkerboard density wave.