I repeatedly heard that K(F\_1) is the sphere spectrum. Does anyone know about the proof and what that means? 



K(F_1) = sphere spectrum?
I understand that this is because GLn(F1) is supposed to be Sigman, the symmetric group on n letters. Thus K(F1) = K(finite sets) which is the sphere spectrum by the Barratt-Priddy-Quillen-Segal theorem.


But I have no idea why GLn(F1) should be Sigman...


