  For a finite group $G$ and $\Bbbk$ an algebraically closed field of
characteristic zero we consider Artin-Schelter regular algebras $A$ on which
the Drinfeld double $D(G)$ acts inner faithfully, and its associated algebras
of invariants $A^{D(G)}$. Explicit computations for the cases when $G$ is the
(generalized) quaternion group of order 8 and 16 are given.
