Algebraic K-theory is an invariant of ring spectra, and more generally Waldhausen categories, that takes values in spectra. If the input is a ring spectrum with G-action, or more generally a Waldhausen category with G-action, we show how to produce a genuinely equivariant spectrum as a result. The key constructions are a categorical version of homotopy fixed points, and the technology of spectral Mackey functors. The most natural construction from a category with G-action, only gives a “coarse” version of equivariant A-theory and we need to work a little harder to promote this to a construction that has a tom Dieck-style splitting on the fixed point spectra.