  We study electrons hopping on a kagome lattice at third filling described by
an extended Hubbard Hamiltonian with on-site and nearest-neighbour repulsions
in the strongly correlated limit. As a consequence of the commensurate filling
and the large interactions, each triangle has precisely two electrons in the
effective low energy description, and these electrons form chains of different
lengths. The effective Hamiltonian includes the ring exchange around the
hexagons as well as the nearest-neighbor Heisenberg interaction. Using large
scale exact diagonalization, we find that the effective model exhibits two
different phases: If the charge fluctuations are small, the magnetic
fluctuations confine the charges to short loops around hexagons, yielding a
gapped charge ordered phase. When the charge fluctuations dominate, the system
undergoes a quantum phase transition to a resonating plaquette phase with
ordered spins and gapless spin excitations. We find that a peculiar
conservation law is fulfilled: the electron in the chains can be divided into
two sublattices, and this division is conserved by the ring exchange term.
