  We study closed bosonic strings propagating both in a flat background with
constant H-flux and in its T-dual configurations. We define a conformal field
theory capturing linear effects in the flux and compute scattering amplitudes
of tachyons, where the Rogers dilogarithm plays a prominent role. For the
scattering of four tachyons, a fluxed version of the Virasoro-Shapiro amplitude
is derived and its pole structure is analyzed. In the case of an R-flux
background obtained after three T-dualities, we find indications for a
nonassociative target-space structure which can be described in terms of a
deformed tri-product. Remarkably, this product is compatible with crossing
symmetry of conformal correlation functions. We finally argue that the R-flux
background flows to an asymmetric CFT.
