  We define the C^*-action on moduli spaces of reductive representations of
fundamental groups of quasi-compact Kaehler manifolds by solving
Hermitian-Yang-Mills equation. As applications in algebraic geometry we show a
non-abelian Hodge (p,q)-type theorem for families of quasi-projective
manifolds. We also prove that any discrete sub group of a Lie group of rank >1
that is not of Hodge type can't be the fundamental group of a quasi-compact
Kaehler manifold.
