If there was no UV mapping before grouping, there wont automatically be any UV mapping after. It’s a quite logical behavior, except that it isn’t very clearly conveyed whether a face has UV mapping or not.
Edit: Wait, I’ve must have misunderstood this. You start with a UV mapped face, change the drawing axes, and then make a group, where the texture has the same rotation it had in the first step, but relative to other axes? I think this is related to the Axes Tool not changing the local axes of the drawing context being edited, but changing the “global” drawing axes.