A cooling-air supply device for a gas turbine, in particular an aircraft gas turbine, including a cooling air chamber, that is disposed about a turbine shaft of the gas turbine, at least one cooling-air inlet opening, and at least one cooling-air outlet orifice; the cooling-air supply device having a first and a second axial bounding wall, and a peripheral wall that joins the two axial bounding walls, which, together, form the cooling air chamber; in at least one of the axial bounding walls, a plurality of cooling-air outlet orifices being provided, which are circumferentially distributed about the turbine shaft and are adapted to allow the cooling air to essentially be discharged from the individual cooling-air outlet orifices in the direction of rotation of the gas turbine. In the axial direction, the respective axial bounding wall having the cooling-air outlet orifices has a layer-type structure; the cooling-air outlet orifices being formed by deformation of at least one first cooling air chamber-side layer and by deformation of at least one second, turbine-side layer.