K-theory spectrum

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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 $\backslash Sigma\; R$ for the suspension of R,

:$(K\_R)\_n\; =\; K\_0(\backslash Sigma^n\; R)\; \backslash times\; BGL(\backslash Sigma^n\; R)^+$,

where "+" means the Quillen's + construction.Dominique Arlettaz, Algebraic K-theory of rings from a topological view point [http://www.math.uiuc.edu/K-theory/0420/] By definition, $K\_i(R)\; =\; \backslash pi\_i(K\_R)$.