K-theory spectrum

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

$(K_{R})_{n}=K_{0}(\Sigma ^{n}R)\times BGL(\Sigma ^{n}R)^{+}$,

where "+" means the Quillen's + construction. By definition, $K_{i}(R)=\pi _{i}(K_{R})$.