### K-Theory of non-linear projective toric varieties, by Thomas Huettemann

By analogy with algebraic geometry, we define a category of non-linear sheaves
(quasi-coherent homotopy-sheaves of topological spaces) on projective toric
varieties and prove a splitting result for its algebraic K-theory,
generalising earlier results for projective spaces. The splitting is expressed
in terms of the number of interior lattice points of dilations of a polytope
associated to the variety. The proof uses combinatorial and geometrical
results on polytopal complexes. The same methods also give an elementary
explicit calculation of the cohomology groups of a projective toric variety
over any commutative ring.

Thomas Huettemann <huette@uni-math.gwdg.de>