Permutation resolutions for Specht modules of Hecke algebras

In Boltje and Hartmann (2011) [BH], a chain complex was constructed in a combinatorial way which conjecturally is a resolution of the (dual of the) integral Specht module for the symmetric group in terms of permutation modules. In this paper we extend the definition of the chain complex to the integral Iwahori Hecke algebra and prove the same partial exactness results that were proven in the symmetric group case.