Dualities in CHL-models

We define a very general class of CHL-models associated with any string theory S (bosonic or supersymmetric) compactified on an internal CFT C×Td. We take the orbifold by a pair (g,δ), where g is a (possibly non-geometric) symmetry of C and δ is a translation along Tn. We analyze the T-dualities of these models and show that in general they contain Atkin-Lehner type symmetries. This generalizes our previous work on N=4 CHL-models based on heterotic string theory on T6 or type II on K3×T2, as well as the 'monstrous' CHL-models based on a compactification of heterotic string theory on the Frenkel-Lepowsky-Meurman CFT V♮.