Jordan correspondence and block distribution of characters

We complete the determination of the $\mathrm{\ell }$-block distribution of characters for quasi-simple exceptional groups of Lie type up to some minor ambiguities relating to non-uniqueness of Jordan decomposition. For this, we first determine the $\mathrm{\ell }$-block distribution for finite reductive groups whose ambient algebraic group defined in characteristic different from $\mathrm{\ell }$ has connected centre. As a consequence we derive a compatibility between $\mathrm{\ell }$-blocks, $e$-Harish-Chandra series and Jordan decomposition. Further we apply our results to complete the proof of Robinson’s conjecture on defects of characters.