Let $G$ be a finite subgroup of $SL_2(\mathbb{C})$ acting on $\mathbb{C}^2=Spec\mathbb{C}[x,y]$. The classical McKay correspondence gives a 1-1 correspondence between nontrivial irreducible representations of $G$, nontrivial maximal Cohen-Macaulay modules of $\mathbb{C}[x,y]^G$, and irreducible components of the exceptional divisor of the minimal resolution of singularities $\pi\colon Y\to \bC^2/G$. There is also a derived version of this correspondence which says that $D^b_G(\mathbb{C}[x,y])\simeq D^b(Y)$. If $G$ a finite subgroup of $GL_2(\mathbb{C})$ but not $SL_2(\mathbb{C}$ and contains no reflections, analogous versions of these correspondences are known. In this talk, I will discuss results on the derived version of this correspondence for some finite subgroups of $GL_2(\mathbb{C})$ that are generated by reflections and discuss connections to work on the algebraic version of the correspondence in this setting due to Buchweitz-Faber-Ingalls. This is joint work with Anirban Bhaduri, Yael Davidov, Eleonore Faber, Katrina Honigs, Eric Overton-Walker, and Dylan Spence.