  Borel's rank theorem identifies the ranks of algebraic $K$-groups of the ring
of integers of a number field with the orders of vanishing of the Dedekind zeta
function attached to the field. Following the work of Gross, we establish a
version of this theorem for Artin $L$-functions by considering equivariant
algebraic $K$-groups of number fields with coefficients in rational Galois
representations. This construction involves twisting algebraic $K$-theory
spectra with rational equivariant Moore spectra. We further discuss integral
equivariant Moore spectra attached to Galois representations and their
potential applications in $L$-functions.
