Given a semi-simple compact Lie group G, the Bott-Samelson resolutions are (non-canonical) desingularizations of certain subspaces inside the Flag varieties for G. We will construct a topological group \tilde{G} which will provide a universal solution to all possible Bott-Samelson resolutions for G. The group \tilde{G} will be shown to relate naturally to a class of groups known as Kac-Moody groups. Kac-Moody groups are a natural extension of the class of semi-simple compact Lie groups, and contain many other interesting examples like Loop groups. We will study the topology of the group \tilde{G}, and compare it to the topology of G. Time permitting, I will outline the proof of the main results using the theory of buildings.