We present an approach to interacting quantum many-body systems based on the notion of quantum groups,also known as q-deformed Lie algebras. In particular, we show that if the symmetry of a free quantum particlecorresponds to a Lie group G, in the presence of a many-body environment this particle can be described bya deformed group, Gq . Crucially, the single deformation parameter, q, contains all the information about themany-particle interactions in the system. We exemplify our approach by considering a quantum rotor interactingwith a bath of bosons, and demonstrate that extracting the value of q from closed-form solutions in the perturbativeregime allows one to predict the behavior of the system for arbitrary values of the impurity-bath coupling strength,in good agreement with non-perturbative calculations. Furthermore, the value of the deformation parameterallows to predict at which coupling strengths rotor-bath interactions result in a formation of a stable quasiparticle.The approach based on quantum groups does not only allow for a drastic simplification of impurity problems, butalso provides valuable insights into hidden symmetries of interacting many-particle systems.