  We extend the techniques in [BKK] to the non-simply-laced situation, and
calculate explicit special values of parabolic affine inverse Kazhdan-Lusztig
polynomials for subregular nilpotent orbits. We thus obtain explicit character
formulas for certain irreducible representations of affine Lie algebras. To do
so, using the geometry of the Springer resolution, we identify the cell
quotient of the anti-spherical module over $\widehat{W}$ corresponding to the
subregular cell with a certain one-dimensional extension of a module defined by
Lusztig in [Lus83]. We describe the canonical basis in this module
geometrically and present an explicit description of the corresponding objects
in the derived category of equivariant coherent sheaves on the Springer
resolution. They correspond to irreducible objects in the heart of a certain
$t$-structure that we describe using an equivariant version of the derived
McKay correspondence.
