A high-pressure switching valve includes a stator and a rotor. The stator includes a plurality of ports where each port is connected at one end to a port connection and having at another end a predetermined port opening cross section at a stator end face of the stator. The rotor includes a rotor end face and at least one or a plurality of grooves. The rotor can be configured to have a rotary position with respect to the stator where two predetermined port opening cross sections connect to one of the grooves in a pressure-tight manner. The rotor and the stator can be pressed together in a sealing manner at the rotor end face and the stator end face in regions away from the port opening cross sections and the at least one or a plurality of grooves. The rotor and the stator each include a hard material. The rotor can be configured to wobble or tilt with respect to a rotational axis of the rotor.