I will present a hyperboloidal initial value problem for energy-supercritical co-rotational wave maps with large initial data. For every odd supercritical dimension, we establish the nonlinear asymptotic stability of an explicitly known self-similar global solution under suitable perturbations. The proof is based on translation to a related blowup problem via Kelvin inversion. If time permits, I will comment on the implications on the role of the explicit solution in regards to long-term dynamics concerning scattering and blowup. This talk is based on ongoing research with Roland Donninger.