The real K-groups of SO(n) for n\(\equiv 3,4\) and 5 mod 8 (Q1105232)

The author determines the algebra structure of \(KO^*(SO(n))\), the real K-theory of the special orthogonal groups SO(n) for \(n\equiv 3,4,5 mod 8\). This paper is a continuation of ibid. 21, 789-808 (1984; Zbl 0553.55002) where the author handled the cases \(n\equiv 0,1,7 \bmod 8\). Essentially the same methods (\({\mathbb{Z}}/2\)-equivariant KO-theory, known results on KO\({}^*(P_ n{\mathbb{R}})\) and \(KO^*(Spin(n))\)) are used. The paper also contains tables for the algebra structure of \(KO^*(P_ n{\mathbb{R}})\) (n as above).