The present invention relates to a switchable actuation device (100) for a gas exchange valve. The switchable actuation device (100) comprises a two-piece rocker arm (10). Said rocker arm comprises a first rocker arm portion (1a), which is mounted pivotably about a rocker arm shaft (2) and to which a bearing sleeve (1a1) is fastened concentrically with the rocker arm shaft (2), and a second rocker arm portion (1b) mounted pivotably on the bearing sleeve (1a1). Furthermore, both the first and the second rocker arm portions (1a, 1b) each comprise a cut-out (3a, 3b), wherein a locking element (4a) of a coupling device (4) of the switchable actuation device (100) can optionally be brought into and out of engagement with the two cut-outs (3a, 3b). An actuation of the poppet valve, preferably a change between a closed position and an open position of the poppet valve, is interrupted if the locking element (4a) is not in engagement with the two cut-outs (3a, 3b). The invention also relates to an internal combustion engine (20) and a motor vehicle (30).