Abstract: After a brief discussion of definitions and known results
regarding A^1-derived categories, we will introduce the notion of cellular
A^1-homology of a scheme endowed with a ``nice" stratification. We will
then describe how cellular A^1-homology can be used to give new
computations of A^1-homology sheaves by considering the stratifications
given by the Bruhat decomposition. The talk is based on joint work in
progress with Fabien Morel.