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 $$\Sigma R$$ 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, $$K_i(R) = \pi_i(K_R)$$.