Exhaust-gas turbocharger having a ball-cock waste-gate valve with a stress-relieved crank arm

An exhaust-gas turbocharger, comprising:

• a turbine housing having a turbine housing wall;
• a wastegate valve disposed in said turbine housing, said wastegate valve being a ballcock-type valve having a spherical-segment-shaped closing element;
• and
• an actuating crank having a crank arm to which said closing element is fastened, and a crank spindle integrally connected to said crank arm, said actuating crank mounted in said turbine housing wall so as to be rotatable about a crank spindle axis of rotation, said actuating crank further having an abutment shoulder disposed in a transition region between said crank spindle and said crank arm, said crank arm having a flexural-stress relief pocket formed therein, wherein adjoining said abutment shoulder on an inner side of said crank arm directed toward said turbine housing wall there is disposed said flexural-stress relief pocket for effecting a more uniform distribution of flexural stresses in said transition region between said crank arm and said crank spindle.