Non-connective delooping of K-theory of an \(A_{\infty}\) ring space (Q1112378)

The suspension of rings [\textit{J. B. Wagoner}, Topology 11, 349-370 (1972; Zbl 0276.18012)] is extended to a construction on \(A_{\infty}\)-ring spaces. It is shown that this construction leads to a nonconnective delooping of the K-theory of an \(A_{\infty}\)-ring space. The negative K-groups given by this delooping then depend only on the ring of components of the \(A_{\infty}\)-ring space. The construction is also being used in Hermitian K-theory of \(A_{\infty}\)-ring spaces with involution, which has applications to spaces of self homotopy equivalences of manifolds.