the algebraic k theory space $k(r)$ is defined as a topological group completion, which on $\pi_0$ is just the usual algebraic group completion of a monoid which yields $k_0(r)$. amazingly, it turns out that this space not only has a multiplication on it which is associative and commutative up to homotopy, but it is an infinite loop space. this means that it represents a spectrum (the stable analogue of a space), and therefore a cohomology theory. we construct equivariant algebraic k-theory for g-rings. however, spectra with g-action (called naive g-spectra) are not robust enough for stable homotopy theory, and the objects of study in equivariant stable homotopy theory are genuine g-spectra, which correspond to cohomology theories graded on representations. our construction of ``genuine" equivariant algebraic k-theory recovers as its fixed points the k-theory of twisted group rings, and as particular cases equivariant topological real and complex k-theory, atiyah's real k-theory and statements previously formulated in terms of naive g-spectra for galois extensions. for example, we can reinterpret the map from the quillen-lichtenbaum conjecture and the assembly map from carlsson's conjecture in terms of genuine g-spectra and their fixed points. we will not assume background in topology and will explain all the concepts from homotopy theory that arise in the talk.