Mapping class group actions on the cohomology of configuration spaces of surfaces

Let X be a closed oriented surface of genus at least 2 and P a finite subset of X. We bound the action of the mapping class group of (X,P) on the rational cohomology groups of the ordered configuration spaces F_n(X-P) of X-P. In particular, we show that, when #P < 2, the diagonal action of the mapping class group on the direct sum of the H^n(F_n(X-P)) is faithful, and determine its kernel when #P > 1.