On Previdi's delooping conjecture for K-theory

We prove a modified version of Previdi's conjecture stating that the Waldhausen space (K-theory space) of an exact category is delooped by the Waldhausen space (K-theory space) of Beilinson's category of generalized Tate vector spaces. Our modified version states the delooping with nonconnective K-theory spectra, extending and almost including Previdi's original statement. As a consequence we obtain that the negative K-groups of an exact category are given by the 0th K-groups of the idempotent-completed iterated Beilinson categories, extending a theorem of Drinfeld that the first negative K-group of a ring is isomorphic to the 0th K-group of the exact category of Tate modules.