The Twisted K-Theory of p-Completed Classifying Spaces

In this talk we will give a description of the twisted K-theory of the p-completion of the classifying space of a finite group, and more generally, for classifying spaces of p-local finite groups. We will begin by introducing representations of p-groups which are invariant under fusion, some examples and a completion theorem relating them to the K-theory of a p-completed classifying space. After this, we consider rings of twisted representations and an alternative interpretation of twisted K-theory. Both objects will be interpreted in terms of central extensions of p-local finite groups, allowing us to give a completion theorem for twisted K-theory. This is joint work with Noe Barcenas.
 
We will end with some questions regarding the behaviour of fusion-invariant representations.