  We introduce analogues of Soergel bimodules for complex reflection groups of
rank one. We give an explicit parametrization of the indecomposable objects of
the resulting category and give a presentation of its split Grothendieck ring
by generators and relations. This ring turns out to be an extension of the
Hecke algebra of the reflection group $W$ and a free module of rank $|W|
(|W|-1)+1$ over the base ring. We also show that it is a generically semisimple
algebra if defined over the complex numbers.
