I am studying algebraic K-theory, currently focusing on its applications to the geometry of formal loop spaces. A certain class of infinite dimensional vector bundles, called Tate vector bundles, plays a crucial role in this context. I showed in my Ph.D. thesis that there is a natural connection between Tate vector bundles and a certain kind of principal bundles, called torsos over the K-theory sheaf. To formulate and prove this connection I used the recently developed theory of infinity topoi, which provides a higher categorical framework with a very wide and flexible geometric scope.