A stable approach to an unstable homotopy spectral sequence

Recently, Bendersky and Thompson introduced a spectral sequence which, for many spaces X, converges to the v1-periodic homotopy groups of X. It is proved that the E2-term of this spectral sequence is often given by Ext in the category of stable p-adic Adams modules of QK1(X;Zp∧)/im(ψp). We compute this spectral sequence when p=2 and X is the exceptional Lie group F4, yielding as a new result the 2-primary v1-periodic homotopy groups of F4. Some new general results about convergence of this spectral sequence are also proved.