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We extend the techniques in [BKK] to the non-simply-laced situation, andcalculate explicit special values of parabolic affine inverse Kazhdan-Lusztigpolynomials for subregular nilpotent orbits. We thus obtain explicit characterformulas for certain irreducible representations of affine Lie algebras. To doso, using the geometry of the Springer resolution, we identify the cellquotient of the anti-spherical module over $\widehat{W}$ corresponding to thesubregular cell with a certain one-dimensional extension of a module defined byLusztig in [Lus83]. We describe the canonical basis in this modulegeometrically and present an explicit description of the corresponding objectsin the derived category of equivariant coherent sheaves on the Springerresolution. They correspond to irreducible objects in the heart of a certain$t$-structure that we describe using an equivariant version of the derivedMcKay correspondence.

Affine Kazhdan-Lusztig polynomials on the subregular cell in non simply-laced Lie algebras: with an application to character formulae