A coated body and a process for producing a layer of hard material on a substrate are described. The body comprises a substrate (30) and a layer of hard material (36) which has been applied to the substrate (30) and at least partly covers the body. The layer of hard material comprises the metallic elements Al, Cr and Si and also nonmetallic elements selected from the group consisting of B, C, N, O. The atomic proportion of oxygen among the nonmetallic elements is greater than 30%. The layer of hard material is deposited on the substrate by means of magnetron atomization.