  Let $\Sigma_{g,n}$ be a compact oriented surface of genus $g$ with $n$ open
disks removed. The graph algebra $\mathcal{L}_{g,n}(H)$ was introduced by
Alekseev--Grosse--Schomerus and Buffenoir--Roche and is a combinatorial
quantization of the moduli space of flat connections on $\Sigma_{g,n}$. We
construct a projective representation of the mapping class group of
$\Sigma_{g,n}$ using $\mathcal{L}_{g,n}(H)$ and its subalgebra of invariant
elements. Here we assume that the gauge Hopf algebra $H$ is finite-dimensional,
factorizable and ribbon, but not necessarily semi-simple. We also give explicit
formulas for the representation of the Dehn twists generating the mapping class
group; in particular, we show that it is equivalent to a representation
constructed by V. Lyubashenko using categorical methods.
