An exhaust-gas turbocharger includes: an exhaust-gas turbocharger housing having a turbine housing, a compressor housing, and a bearing housing; a turbine in the turbine housing; a compressor in the compressor housing; and a shaft rotatably mounted in the bearing housing by which the turbine and the compressor are rigidly connected, at least one channel having an inlet opening and an outlet opening being formed inside the shaft, the inlet opening and/or the outlet opening being arranged in a radial direction on a circumference of the shaft between the turbine and the compressor. The at least one channel is part of a channel system of an exhaust-gas recirculation system, a reducing agent infeed, or a secondary air infeed. For the secondary air infeed, an interior space of the compressor housing is in fluidic connection with an interior space of the turbine housing.