  We declare briefly several interesting features of the quantum relativistic
Toda chain at N-th root of unity. We consider the finite dimensional
representation of the Weyl algebra. The origin of the features mentioned is
that we consider simultaneously the quantum finite dimensional part and the
classical dynamics of N-th powers of Weyl's elements. As the main result, using
the technique of Q-operators, we establish a correspondence between the
separation of variables in the quantum model and the Baecklund transformations
of its classical counterpart.
