K-theory spectrum

In mathematics, given a ring R, the K-theory spectrum of R is an Ω-spectrum $K_R$ whose nth term is given by, writing $\mathrm{\Sigma }R$ for the suspension of R,

$(K_R{)}_n=K_0({\mathrm{\Sigma }}^{n}R)\times BGL({\mathrm{\Sigma }}^{n}R{)}^{+}$,

where "+" means the Quillen's + construction. By definition, $K_i(R)={\pi }_i(K_R)$.