Abstract :
Using Thomason and Trobaughʹs localization theorem for theK-theory of a scheme, we study theK-theory of the category of vector bundles with endomorphisms over a scheme. The results generalize those of Grayson when the scheme is affine. We also give an example showing that the Mayer–Vietoris sequence does not hold for theK-theory of vector bundles with endomorphisms, which indicates that theK-theory of vector bundles with endomorphisms is a global theory (not determined by local data).
