Airbag and airbag module for a motor vehicle having such an airbag

An airbag module for a motor vehicle, comprising

• an airbag (14),
• a gas generator (32) for inflating the airbag (14), and
• a control unit (36) for activating the gas generator (32),
• wherein the airbag comprises:
• an impact wall (20) which, in an installed and unfolded state of the airbag (14), faces a vehicle occupant (18), and
• a circumferential wall (22) which is connected to the impact wall (20) and, in the installed and unfolded state of the airbag (14), extends between the impact wall (20) and a vehicle part (10),
• wherein the circumferential wall (22) is made with multiple layers at least in sections and forms at least one annular tube (23) which delimits an annular inflatable first airbag volume (V1),
• wherein a radially inner layer (26) of the circumferential wall (22) together with the impact wall (20) delimits an inflatable second airbag volume (V2) that is separate from the first airbag volume (V1), and
• wherein boundary conditions for applying generator gas to the first airbag volume (V1) or to the second airbag volume (V2) are deposited in the control unit (36).