Decomposition matrices for exceptional groups at d=4d=4

We determine the decomposition matrices of unipotent ℓ  -blocks of defect Φ42 for exceptional groups of Lie type up to a few unknowns. For this we employ the new cohomological methods of the first author, together with properties of generalised Gelfand–Graev characters which were recently shown to hold whenever the underlying characteristic is good.