  In this note, we compute the split Grothendieck ring of a generalized
category of Soergel bimodules of type $A_2$, where we take one generator for
each reflection. We give a presentation by generators and relations of it and a
parametrization of the indecomposable objects in the category, by realizing
them as rings of regular functions on certain unions of graphs of group
elements on a reflection faithful representation.
