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Jul 2, 2012 at 4:49 comment added Sean Tilson Also, that spectral sequence works the same for any generalized cohomology theory. The only issue might be convergence if it is not connective (or bounded below rather).
Jul 2, 2012 at 4:47 comment added Sean Tilson I was just about to suggest this. Their construction is pretty explicit. While they are mostly interested in the case where $G=S^1$ you can get the general case by using your favorite model for $EG$ and following their construction.
Jul 1, 2012 at 12:55 comment added Akhil Mathew This paper looks pretty interesting. Thanks.
Jul 1, 2012 at 3:25 history answered Craig Westerland CC BY-SA 3.0