  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 finest dominated
splitting. Therefore the restriction of the generic cocycle to a subbundle of
the finest dominated splitting is uniformly subexponentially quasiconformal.
This extends a previous result for SL(2,R)-cocycles due to Avila and the
author.
