  We show that the $G$-equivariant coherent derived category of $D$-modules on
$\mathfrak{g}$ admits an orthogonal decomposition in to blocks indexed by
cuspidal data (in the sense of Lusztig). Each block admits a monadic
description in terms a certain differential graded algebra related to the
homology of Steinberg varieties, which resembles a "triple affine" Hecke
algebra. Our results generalize the work of Rider and Rider--Russell on
constructible complexes on the nilpotent cone, and the earlier work of the
author on the abelian category of equivariant $D$-modules on $\mathfrak{g}$.
However, the algebra controlling the entire derived category of $D$-modules
appears to be substantially more complicated than either of these special
cases, as evidenced by the non-splitting of the Mackey filtration on the monad
controlling each block.
