A compressor rotor is provided having a rotor blade groove thereon and also includes a device for cooling the rotor in the region of a compressor rotor exit. Efficient cooling is achieved by the compressor rotor, in a compressor rotor exit region, having a ring which is pushed concentrically, and at a distance, forming a gap, over a rotor disk of the rotor, and is fastened on the disk, by the rotor blades, in the compressor rotor exit region, being inserted into corresponding grooves on the ring and being retained there, by first means for directing an axial flow of cooling medium from the compressor rotor exit through the ring, and by second means for deflecting the cooling medium which issues from the ring such that the cooling medium flows back in the axial direction through the gap between the ring and the rotor disk, encompassed by the ring.