Given a vertex operator algebra with a group G of symmetries, there is the notion of g-twisted modules. But moreover for G a Lie group there is (or should be) a notion of twisted modules by a G-connection. For connections with regular singularity, this recovers the g-twisted
modules, with g the monodromy, but we can also study irregular singularities. In this talk we discuss some basic questions in this endeavour, and we give interesting results for the triplet vertex algebra, whose category of representations is equivalent to the small quantum group of sl2. In particular, for a regular singularity with nilpotent monodromy g we have previously found twisted modules to be large tilting modules, and for an irregular singularity we find in our
upcoming work Whittaker modules.

Both is joint work with B. Feigin.