K-theory spectrum

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

[math]\displaystyle{ (K_R)_n = K_0(\Sigma^n R) \times BGL(\Sigma^n R)^+ }[/math],

where "+" means the Quillen's + construction. By definition, [math]\displaystyle{ K_i(R) = \pi_i(K_R) }[/math].