Monodromy for systems of vector bundles and multiplicative preprojective algebras

We study systems involving vector bundles and logarithmic connections on Riemann surfaces and linear algebra data linking their residues. This generalizes representations of deformed preprojective algebras. Our main result is the existence of a monodromy functor from such systems to representations of a multiplicative preprojective algebra. As a corollary, we prove that the multiplicative preprojective algebra associated to a Dynkin quiver is isomorphic to the usual preprojective algebra.