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A certain class of unitary representations of U_q(sl(2,R)) has the propertyof being simultanenously a representation of U_{tilde{q}}(sl(2,R)) for aparticular choice of tilde{q}(q). Faddeev has proposed to unify the quantumgroups U_q(sl(2,R)) and U_{tilde{q}}(sl(2,R)) into some enlarged object forwhich he has coined the name ``modular double''. We study the R-operator, theco-product and the Haar-measure for the modular double of U_q(sl(2,R)) andestablish their main properties. In particular it is shown that theClebsch-Gordan maps constructed in [PT2] diagonalize this R-operator.Comment: 27 pages, LaTex (smfart.sty

R-Operator, Co-Product and Haar-Measure for the Modular Double of