  In this paper, and a second part to follow, we complete the programme
(initiated more than 15 years ago) of determining the decomposition numbers and
verifying James' Conjecture for Iwahori--Hecke algebras of exceptional type.
The new ingredients which allow us to achieve this aim are:
  - the fact, recently proved by the first author, that all Hecke algebras of
finite type are cellular in the sense of Graham--Lehrer, and
  - the explicit determination of $W$-graphs for the irreducible (generic)
representations of Hecke algebras of type $E_7$ and $E_8$ by Howlett and Yin.
  Thus, we can reduce the problem of computing decomposition numbers to a
manageable size where standard techniques, e.g., Parker's {\sf MeatAxe} and its
variations, can be applied. In this part, we describe the theoretical
foundations for this procedure.
