  A group action on the input ring or category induces an action on the
algebraic $K$-theory spectrum. However, a shortcoming of this naive approach to
equivariant algebraic $K$-theory is, for example, that the map of spectra with
$G$-action induced by a $G$-map of $G$-rings is not equivariant. We define a
version of equivariant algebraic $K$-theory which encodes a group action on the
input in a functorial way to produce a $genuine$ algebraic $K$-theory
$G$-spectrum for a finite group $G$. The main technical work lies in studying
coherent actions on the input category. A payoff of our approach is that it
builds a unifying framework for equivariant topological $K$-theory, Atiyah's
Real $K$-theory, and existing statements about algebraic $K$-theory spectra
with $G$-action. We recover the map from the Quillen-Lichtenbaum conjecture and
the representational assembly map studied by Carlsson and interpret them from
the perspective of equivariant stable homotopy theory.
