Abstract
Twin buildings are combinatorial objects which were introduced by Ronan and Tits in the late 1980s. Their definition was motivated by the theory of Kac-Moody groups over fields and they are natural generalizations of spherical buildings. Spherical buildings were classified by Tits in the 1970s and this result is based on a local-to-global result on spherical buildings. Tits asked the question whether a similar result holds for twin buildings. This has been confirmed by Mühlherr and Ronan under an additional assumption which is not satisfied for twin buildings associated with Kac-Moody groups over F2𝐹2. We give a construction of groups of Kac-Moody type over F2𝐹2 which shows that the local-to-global result does not hold in general. We will discuss some applications including finiteness properties and Property T𝑇.