For a compact, simply connected Lie group G with maximal torus T, the Flag variety G/T contains sub varieties know as Schubert varieties. These varieties admit (non-canonical) resolutions known as Bott-Samelson resolutions. In my talk I will construct a topological group \tilde{G} that contains T and maps to G, with the property that \tilde{G}/T encodes all possible Bott-Samelson resolutions of G. I will show how the group \tilde{G} naturally fits into the framework of Kac-Moody groups, and also describe the structure of the projection map from \tilde{G}/T to G/T under any complex oriented homology theory. Time permitting, I will show how to obtain the main results by studying the (partial) topological buildings for G.