Kac-Moody Groups and Cosheaves on Davis Building

We investigate smooth representations of complete Kac-Moody groups. We approach representation theory via geometry, in particular, the group action on the Davis realisation of its Bruhat-Tits building. Our results include an estimate on projective dimension, localisation theorem, unimodularity and homological duality.
Comment: 28 pages. Version 3: some minor corrections, actions on simplicial sets are explained. Version 4: minor corrections