Vladimir Manuilov (Moscow State University)
A well-known construction allows to get vector bundles over classifying spaces out of finite dimensional representations of groups, but not too many of them. A similar construction due to Mishchenko allows to do the same out of something more general than genuine representations, namely of almost representations, when the group relations are satisfied not exactly. Even a simple example of an abelian group on two generators shows that the resulting vector bundles can be non-trivial. We will discuss relations between almost representations and asymptotic ones and the question of exhausting K-groups of classifying spaces by vector bundles coming from asymptotic representations.