An exhaust
turbocharger has a housing, in which a shaft is mounted by bearings, which carries a
turbine wheel, on the one hand, and a compressor wheel, on the other hand. An
electric machine has a rotor and a
stator. The rotor is secured on the shaft for conjoint rotation therewith and the
stator surrounds the rotor radially on the outside. A sleeve, which supports the rotor radially and axially, is arranged between the
stator and the rotor. The sleeve has at least one fluid duct, by way of which a
cooling fluid can be guided toward the bearings of the shaft.