  The pseudo--rigid body represents an example of a constrained system with a
nonunimodular gauge group. This system is treated along the guidelines of an
algebraic constraint quantization scheme which focusses on observable
quantities, translating the vanishing of the constraints into representation
conditions on the algebra of observables. The constraint which is responsible
for the nonunimodularity of the gauge group is shown not to contribute to the
observable content of the constraints, i.e., not to impose any restrictions on
the construction of the quantum theory of the system. The application of the
algebraic constraint quantization scheme yields a unique quantization of the
physical degrees of freedom, which are shown to form a realization of the
so-called CM(N) model of collective motions.
