We discuss a diagrammatic presentation of the Hecke category and its cellular structure. Using this, we will compute decomposition numbers in Hecke categories and hence determine some tilting characters.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/4234
[3] http://www.mpim-bonn.mpg.de/node/9215