  We define extensions of the $L^2$-analytic invariants of closed manifolds,
called delocalized $L^2$-invariants. These delocalized invariants are
constructed in terms of a nontrivial conjugacy class of the fundamental group.
We show that in many cases, they are topological in nature. We show that the
marked length spectrum of an odd-dimensional hyperbolic manifold can be
recovered from its delocalized $L^2$-analytic torsion. There are technical
convergence questions.
