A pump, comprising: an accommodating housing which forms an accommodating space, which is in particular cup-shaped, with a front-facing wall and a circumferential wall; and a pump insert which is arranged in the accommodating space, wherein the pump insert comprises: - a rotor; - a first housing part and a second housing part, between which the rotor is arranged such that it can rotate about a rotational axis and relative to the first and second housing parts (2, 3); and - a stroke ring which surrounds the rotor and is arranged between the first housing part and the second housing part, wherein a first delivery chamber and a second delivery chamber are formed radially between the stroke ring and the rotor, characterised in that: a first pressure space, which is formed between the front-facing wall of the accommodating housing and the second housing part, is connected to the first delivery chamber via a first outlet channel, and a second pressure space is connected to the second delivery chamber via a second outlet channel; a gasket which is arranged between the second housing part and the circumferential wall seals the first pressure space off from a suction space; and a sealing element which is arranged between the second housing part and the front-facing wall surrounds the second pressure space and seals the first pressure space and the second pressure space off from each other. an accommodating housing which forms an accommodating space, which is in particular cup-shaped, with a front-facing wall and a circumferential wall; and a pump insert which is arranged in the accommodating space, wherein the pump insert comprises: - a rotor; - a first housing part and a second housing part, between which the rotor is arranged such that it can rotate about a rotational axis and relative to the first and second housing parts (2, 3); and - a stroke ring which surrounds the rotor and is arranged between the first housing part and the second housing part, - a rotor; - a first housing part and a second housing part, between which the rotor is arranged such that it can rotate about a rotational axis and relative to the first and second housing parts (2, 3); and - a stroke ring which surrounds the rotor and is arranged between the first housing part and the second housing part, wherein a first delivery chamber and a second delivery chamber are formed radially between the stroke ring and the rotor, characterised in that: a first pressure space, which is formed between the front-facing wall of the accommodating housing and the second housing part, is connected to the first delivery chamber via a first outlet channel, and a second pressure space is connected to the second delivery chamber via a second outlet channel; a gasket which is arranged between the second housing part and the circumferential wall seals the first pressure space off from a suction space; and a sealing element which is arranged between the second housing part and the front-facing wall surrounds the second pressure space and seals the first pressure space and the second pressure space off from each other. a first pressure space, which is formed between the front-facing wall of the accommodating housing and the second housing part, is connected to the first delivery chamber via a first outlet channel, and a second pressure space is connected to the second delivery chamber via a second outlet channel; a gasket which is arranged between the second housing part and the circumferential wall seals the first pressure space off from a suction space; and a sealing element which is arranged between the second housing part and the front-facing wall surrounds the second pressure space and seals the first pressure space and the second pressure space off from each other.