Abstract :
The purpose of this note is to give another example of applications of the general results of an earlier paper. Here we apply the general localization theorem in K-theory of admissible abelian categories obtained there to twisted projective lines and obtain a long exact sequence relating the K-theory of twisted polynomial and twisted Laurent polynomial rings: · · · → Kn+1(Rφ[t, t−1]) →, Kn(R) circled plus Kn(R) → Kn(Rφ[t]) circled plus Kn(Rφ[t−1]) → Kn(Rφ[t, t−1]) → · · · .