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In this note, we give a general method to obtain unstable motivic cellstructures, following Wendt's application of the Bialynicki-Birula algebraicMorse theory. We then apply the method to spherical varieties, with specialattention to the case of rank 1, to obtain unstable motivic cell structuresafter a finite number of $\mathbb{P}^1$-suspensions.  This work is a partial derivative of the first two chapters of the author's2016 PhD thesis.

Motivic Cell Structures for Spherical Varieties