The properties of a local spin S=1/2 coupled to K independent wires is studied in the presence of bias voltages which drive the system out of thermal equilibrium. For K≫1, a perturbative renormalization group approach is employed to construct the voltage-dependent scaling function for the conductance and the T matrix. In contrast to the single-channel case, the Kondo resonance is split even by bias voltages small compared to the Kondo temperature T(K), V≪T(K). Besides the applied voltage V, the current-induced decoherence rate Γ≪V controls the physical properties of the system. While the presence of V changes the structure of the renormalization group considerably, decoherence turns out to be very effective in prohibiting the flow towards new nonequilibrium fixed points even in variants of the Kondo model where currents are partially suppressed.
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