  We investigate the canonical quantization of gravity coupled to pointlike
matter in 2+1 dimensions. Starting from the usual point particle action in the
first order formalism, we introduce auxiliary variables which make the action
locally Poincar\'e invariant. A Hamiltonian analysis shows that the gauge group
is actually larger than the Poincar\'e group -- certain additional gauge
constraints are present which act on the matter degrees of freedom. These
additional constraints are necessary to mimic the diffeomorphism invariance
present if the theory is formulated with a spacetime metric. The additional
gauge constraints are realized projectively in the quantum theory, with a phase
in the composition law for finite gauge transformations. That phase is
responsible for the braid invariance of physical observables (holonomies).
