In mathematics, given a ring R, the K-theory spectrum of R is an Ω-spectrum K R {\displaystyle K_{R}} whose nth term is given by, writing Σ R {\displaystyle \Sigma R} for the suspension of R, n = K 0 × B G L + {\displaystyle _{n}=K_{0}\times BGL^{+}},where "+" means the Quillen's + construction. Wikipedia