A1-invariants in Galois cohomology and a claim of Morel
Abstract
We establish a variant of the splitting principle of Garibaldi-Merkurjev-Serre for invariants taking values in a strictly homotopy invariant sheaf. As an application, we prove the folklore result of Morel that pi0 of the motivic localization of the group completion of the stack of finite \'etale schemes is given by the sheaf of unramified Grothendieck-Witt groups.
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