On \(Ad^ *\)-cohomology groups of the classifying spaces of compact Lie groups (Q1088191)

Let G be a compact Lie group, \(G_ 0\) the connected component of the identity and BG the classifying space. Let k be a positive integer and R a proper subring of \({\mathbb{Q}}\) which contains \(k^{-1}\). The author considers the secondary cohomology theory [\textit{L. Smith}, Indiana Univ. Math. J. 23, 899-923 (1974; Zbl 0285.55005)] associated to the stable operation \(1-\psi^ k_*\) (where \(\psi^ k\) is the Adams operation), denotes the theory by \(Ad^*(X;R)\) and proves (i) \(Ad^{2m}(BG;R)=0\) for any integer \(m\neq 0\), and (ii) \(Ad^ 0(BG;R)=0\) if \(| G/G_ 0|\) is invertible in R.