On centrality of K2K2 for Chevalley groups of type EℓEℓ

For a root system Φ of type EℓEℓ and arbitrary commutative ring R   we show that the group K2(Φ,R)K2(Φ,R) is contained in the center of the Steinberg group St(Φ,R)St(Φ,R). In course of the proof we also demonstrate an analogue of Quillen–Suslin local–global principle for K2(Φ,R)K2(Φ,R).