  The Hubbard model constitutes one of the most celebrated theoretical
frameworks of condensed-matter physics. It describes strongly correlated phases
of interacting quantum particles confined in lattice potentials. For bosons,
the Hubbard Hamiltonian has been deeply scrutinised for short-range on-site
interactions. However, accessing longer-range couplings has remained elusive
experimentally. This marks the frontier towards the extended Bose-Hubbard
Hamiltonian that allows insulating ordered phases at fractional lattice
fillings. Here we implement this Hamiltonian by confining semiconductor dipolar
excitons in an artificial two-dimensional square lattice. Strong dipolar
repulsions between nearest neighbouring lattice sites then stabilise an
insulating state at half filling. This characteristic feature of the extended
Bose-Hubbard model exhibits signatures theoretically expected for a
checkerboard spatial order. Our work thus highlights that dipolar excitons
enable controlled implementations of boson-like arrays with strong off-site
interactions, in lattices with programmable geometries and over 100 sites.
