Centrality of K2 for Chevalley groups: a pro-group approach

We prove the centrality of K2(F4, R) for an arbitrary commutative ring R. This completes the proof of the centrality of K2(Φ, R) for any root system Φ of rank ≥ 3. Our proof uses only elementary localization techniques reformulated in terms of pro-groups. Another new result of the paper is the construction of a crossed module on the canonical homomorphism St(Φ, R) → Gsc(Φ, R), which has not been known previously for exceptional Φ.