  We consider general cyclic representations of the 6-vertex Yang-Baxter
algebra and analyze the associated quantum integrable systems, the
Bazhanov-Stroganov model and the corresponding chiral Potts model on finite
size lattices. We first determine the propagator operator in terms of the
chiral Potts transfer matrices and we compute the scalar product of separate
states (including the transfer matrix eigenstates) as a single determinant
formulae in the framework of Sklyanin's quantum separation of variables. Then,
we solve the quantum inverse problem and reconstruct the local operators in
terms of the separate variables. We also determine a basis of operators whose
form factors are characterized by a single determinant formulae. This implies
that the form factors of any local operator are expressed as finite sums of
determinants. Among these form factors written in determinant form are in
particular those which will reproduce the chiral Potts order parameters in the
thermodynamic limit.
