A rear gearshift mechanism for installation on a bicycle frame coaxial with a rear-wheel axis has a base element, a pivot mechanism, a movable element and a chain guide. The base element includes an attachment end for installation on the bicycle frame. A first arm and a second arm of the attachment end are arranged spaced apart from one another in an axial direction and, by an associated adapter which has a thread, are configured for the installation of the gearshift mechanism on an associated bracket portion, in particular a dropout or frame hanger. The first arm is arranged on an inner side of the bracket portion, and the second arm is arranged on an outer side of the bracket portion. The base element is designed with a setting device by which the base element can be pivoted in a chain tensioning direction.