Kristian MOI (Münster): Real and Hermitian algebraic K-theory

In this talk I will present the Real algebraic K-theory construction of Hesselholt and Madsen, and discuss some on-going joint work with Ib Madsen. Real algebraic K-theory is a functor that to a ring A with anti-involution associates a genuine C_2-equivariant spectrum KR(A). Here C_2 denotes the cyclic group of order two. The underlying spectrum of KR(A) has the homotopy type of K(A), the usual K-theory space of A in the sense of Quillen, and the C_2-fixed point spectrum is weakly equivalent to the Hermitian K-theory of A. I will talk about generalizations of known theorems for algebraic K-theory to KR, including delooping results, "fundamental" theorems and group completion.