We show that if two rings have equivalent derived categories, then they have the same algebraic K-theory. Similar results are given for G-theory and for a large class of abelian categories.
Daniel Dugger. Brooke Shipley. "K-theory and derived equivalences." Duke Math. J. 124 (3) 587 - 617, 15 September 2004. https://doi.org/10.1215/S0012-7094-04-12435-2