Generic linear cocycles over a minimal base

We prove that a generic linear cocycle over a minimal base dynamics of finite dimension has the property that the Oseledets splitting with respect to any invariant probability coincides almost everywhere with the ńest dominated splitting. Therefore the restriction of the generic cocycle to a subbundle of the ńest dominated splitting is uniformly subexponentially quasiconformal. This extends a previous result for SL(2;R)-cocycles due to Avila and the author.