A spectral sequence with only one index in Atiyah's paper? I would like to read Atiyah's paper Characters and cohomology of finite groups; but when I started reading the introduction, Atiyah mentions that he will prove that there is a "spectral sequence $\{E^p_r\}$  with $E^p_2 = H^p(G,\mathbb{Z})$ and $E^p_\infty = R_p(G)/R_{p+1}(G)$"
I can't understand what this means, because a spectral sequence is supposed to have $2$ indices, like $E^{p,q}_2$. 
My best guess is that it would be an old notation, for instance that what he denotes $E^p_2$ would the graded module $\displaystyle\bigoplus_{q}E_2^{p,q}$; but I'm not sure, and I would like not to have to guess to understand the paper. 
Is this a common notation, an old notation ? What does it mean ? 
 A: He writes what he means in a section titled 'spectral sequences' at the start of page 34 (end of section 3). He means a sequence of graded complexes $(E_r, d_r)$, with $d_r$ of degree $r$, with specified isomorphisms $H(E_r, d_r) \cong E_{r+1}$. 
He writes this with the meaning you expect (collapsing a bigraded spectral sequence to a single grading) for the usual cohomology-to-K-theory AHSS in propositions 2.4 and 2.6.
However, the target for the spectral sequence you're talking about is the representation ring $R(G)$, which in particular is not a graded object; Atiyah introduces a filtration (which I think is from the dimension of an irrep) and then argues that a spectral sequence converges to this target. 
I am not familiar enough with the paper to tell you how that spectral sequence is constructed. However, I will point out that because $R(G)$ is not naturally graded, it would be odd to have a bigraded spectral sequence converging to it; this would naturally construct a grading (at least on each filtered piece), which seems like it would be odd; I have no idea where it would come from! 
So it seems likely that the SS he constructs does not naturally have a second grading, and that it only fits into the formalism I mentioned at the start of this post. 
