A modified fundamental theorem for algebraic K-theory is established for strongly Z-graded rings, with splittings via shift actions on modules and nil groups identified as reduced K-theory of homotopy nilpotent twisted endomorphisms, plus Mayer-Vietoris and localisation sequences.
A twisted B ass- H eller- S wan decomposition for the algebraic K -theory of additive categories
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The "fundamental theorem" for the algebraic $K$-theory of strongly $\mathbb{Z}$-graded rings
A modified fundamental theorem for algebraic K-theory is established for strongly Z-graded rings, with splittings via shift actions on modules and nil groups identified as reduced K-theory of homotopy nilpotent twisted endomorphisms, plus Mayer-Vietoris and localisation sequences.