Georgia Institute of Technology College of Sciences

It is a classical theorem in algebraic topology that the loop space of a suitable Lie group can be modeled by an infinite dimensional variety, called the loop Grassmannian. It is also well known that there is an algebraic analog of loop Grassmannians, known as the affine Grassmannian of an algebraic groop (this is an ind-variety). I will explain how in motivic homotopy theory, the topological result has the "expected" analog: the Gm-loop space of a suitable algebraic group is A^1-equivalent to the affine Grassmannian.