  In this paper, we generalize the Quillen-Lichtenbaum Conjecture relating
special values of Dedekind zeta functions to algebraic $\mathrm{K}$-groups. The
former has been settled by Rost-Voevodsky up to the Iwasawa Main Conjecture.
Our generalization extends the scope of this conjecture to Artin $L$-functions
of Galois representations of finite, function, and totally real number fields.
The statement of this conjecture relates norms of the special values of these
$L$-functions to sizes of equivariant algebraic $\mathrm{K}$-groups with
coefficients in an equivariant Moore spectrum attached to a Galois
representation.
  We prove this conjecture in many cases, integrally, except up to a possible
factor of powers of $2$ in the non-abelian and totally real number field case.
In the finite field case, we further determine the group structures of their
equivariant algebraic $\mathrm{K}$-groups with coefficients in Galois
representations. At heart, our method lifts the M\"obius inversion formula for
factorizations of zeta functions as a product of $L$-functions, to the
$E_1$-page of an equivariant spectral sequence converging to equivariant
algebraic $\mathrm{K}$-groups. Additionally, the spectral Mackey functor
structure on equivariant $\mathrm{K}$-theory allows us to incorporate certain
ramified extensions that appear in these $L$-functions.
