Equivariant algebraic K-theory is an extension of algebraic K-theory to rings equipped with an action by a finite group G. This dissertation presents calculations of two different families of invariants associated to the equivariant algebraic K-theory of finite fields. The first concerns the case where G is the Galois group of an extension of finite fields. Based on joint work with David Chan, we compute the full collection of equivariant K-groups graded on the Grothendieck group RO(G) of real orthogonal G-representations. Specifically, we show that these K-groups split as the sum of an explicitly computable term and the well-studied RO(G)-graded coefficient groups of ordinary equivariant integral homology. The second concerns connections to K-theoretic invariants of group algebras of finite groups. We prove an induction theorem for the higher algebraic K-groups of group algebras of finite groups over characteristic p finite fields. For a certain class of finite groups, which we call p-isolated, this reduces calculations to calculations for their p-subgroups. For p-isolated groups with Sylow p-subgroups of order p, we produce explicit new calculations of K-groups.