  We introduce a notion of Milnor square of stable $\infty$-categories and
prove a criterion under which algebraic K-theory sends such a square to a
cartesian square of spectra. We apply this to prove Milnor excision and proper
excision theorems in the K-theory of algebraic stacks with affine diagonal and
nice stabilizers. This yields a generalization of Weibel's conjecture on the
vanishing of negative K-groups for this class of stacks.

Algebraic Geometry;K-Theory and Homology