Abstract: I will discuss G-equivariant motivic stable homotopy theory for G finite, and some applications, mostly for G=Z/2. In this case, I will construct a motivic (=algebraic) analogue of Atiyah's real K-theory, and related periodicity theorems (Karoubi-Hornbostel theorems, and a new theorem), and also a solution (in some sense) of the completion problem for Hermitian K-theory. I will also discuss an algebraic (=motivic) version of Landweber's Real cobordism.