I describe an algebraic scheme for quantizing the Ruijsenaars-Schneider

models in the R-matrix formalism. It is based on a special parametrization

of the cotangent bundle over GL(n,C). In new variables

the standard symplectic structure is described by a classical (Frobenius)

r-matrix and by a new dynamical r¯-matrix. Quantizing these

r-matrices, I will exhibit the quantum L-operator algebra and construct

its particular representation corresponding to the RuijsenaarsSchneider

system. I will also indicate a couple of open problems.