This paper presents a relatively simple construction of the algebraic K–theory
presheaf of spectra, which starts with a method of functorially associating a
symmetric spectrum K(M) to an exact category M.
Some applications are displayed: these include a Galois cohomological descent
spectral sequence for the étale K–theory of a scheme (where the Galois group is the
Grothendieck fundamental group), and the Morel–Voevodsky description of
Thomason–Trobaugh K–theory as Nisnevich K–theory in nonnegative degrees. The
is also a spectrum-level description of Voevodsky’s periodicity operator for Nisnevich
K–theory.
