  We complete the canonical quantization of the vacuum Bianchi I model within
the improved dynamics scheme of loop quantum cosmology, characterizing the
Hilbert structure of the physical states and providing a complete set of
observables acting on them. In order to achieve this task, it has been
essential to determine the structure of the separable superselection sectors
that arise owing to the polymeric quantization, and to prove that the initial
value problem obtained when regarding the Hamiltonian constraint as an
evolution equation, interpreting the volume as the evolution parameter, is
well-posed.
