Apparatus for transferring an object from a first station to a second station with a different orientation is provided comprising a stator, a rotor rotatable externally of the stator about an axis of rotation, and at least one retaining member for retaining the object. The retaining member can rotate integrally with the rotor, and is rotatable with respect to the rotor about its own axis of rotation. The stator has a cam profile coupled to and functionally cooperating with at least one axially extending follower which is constrained to the retaining member. The axis of rotation of the retaining member and the axis of extension of the follower are substantially always incident to the axis of rotation of the rotor.