@John: Thanks ! One can also write K(Z(1),2) as the infinite loop space of the second suspension of the EM-spectrum HZ(1) and calculate the homotopy fixed points stably. So pi_0 vanishes as it should.

I'm not really familiar with the unstable situation, where does this spectral sequence come from ?

One thing to note is that an isomorphism of geometric realization does not imply anything about homotopy colimits yet because one needs reedy cofibrant diagrams (in algebras and underlying).

Are you saying the statement about homotopy colimits can be extracted from Thm 8.2 or are you referring to what they do with bar resolutions in the proof ?

I'll have a look at that paper, thanks.

I was aware of the results in "Clifford Modules" but couldn't relate them to Segal's statement. They describe the coefficients in terms of Clifford algebras while Segal talks about actual representing spaces which seems stronger.