The S-matrix of the world-sheet theory of the string in AdS(5)xS(5) is known to admit a deformation where the original symmetry algebra is replaced by the associated quantum group. The case where q, the deformation parameter, is real has been identified as a particular deformation of the Green-Schwarz sigma model known as the "eta-deformation". The case with q a root of unity interpolates between the AdS(5)xS(5) world-sheet theory and its Pohlmeyer reduction. However, an interpretation of this case is still lacking. We will summarize recent work aimed to show that sigma models on (semi-)symmetric spaces F/G admit discrete integrable deformations that can be viewed as deformations of the F/F gauged WZW model. For the AdS(5)xS(5) world-sheet theory, F=PSU(2,2|4) and the resulting theory has just the right amount of kappa-symmetries, which points to the existence of a new fully consistent deformed string background.