The K -functor (Grothendieck group) of the infinite symmetric group

The Grothendieck group K₀() of the group of finite permutations of a countable set is described. All semifinite characters of are described and with their help the cone of representations K ₊ ⁰ () is characterized.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 123, pp. 126–151 (1983).