Homology and<i>K</i>-theory of dynamical systems I. Torsion-free ample groupoids

Given an ample groupoid, we construct a spectral sequence with groupoid homology integer coefficients on the second sheet, converging to K-groups of (reduced) C*-algebra, provided has torsion-free stabilizers and satisfies strong form Baum-Connes conjecture. The construction is based triangulated category approach conjecture developed by Meyer Nest. We also present few applications topological dynamics discuss HK Matui.