  The noncommutative (Cohn) localization S^{-1}R of a ring R is defined for any
collection S of morphisms of f.g. projective left R-modules. We exhibit S^{-1}R
as the endomorphism ring of R in an appropriate triangulated category. We use
this expression to prove that if S^{-1}R is "stably flat over R" (meaning that
Tor^R_i(S^{-1}R,S^{-1}R)=0 for i>0) then every bounded f.g. projective
S^{-1}R-module chain complex D with [D] \in im(K_0(R)-->K_0(S^{-1}R)) is chain
equivalent to S^{-1}C for a bounded f.g. projective R-module chain complex C,
and that there is a localization exact sequence in higher algebraic K-theory
>... --> K_n(R) --> K_n(S^{-1}R) --> K_n(R,S) --> K_{n-1}(R) --> ..., extending
to the left the sequence obtained for n<2 by Schofield. For a noncommutative
localization S^{-1}R of a ring with involution R there are analogous results
for algebraic L-theory, extending the results of Vogel from quadratic to
symmetric L-theory.
