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We extend Matui's notion of almost finiteness to general etale groupoids andshow that the reduced groupoid C*-algebras of minimal almost finite groupoidshave stable rank one. The proof follows a new strategy, which can be regardedas a local version of the large subalgebra argument. The following three arethe main consequences of our result. (i) For any group of (local)subexponential growth and for any its minimal action admitting a totallydisconnected free factor, the crossed product has stable rank one. (ii) Anycountable amenable group admits a minimal action on the Cantor set all whoseminimal extensions form the crossed product of stable rank one. (iii) For anyamenable group, the crossed product of the universal minimal action has stablerank one.

Almost finiteness for general etale groupoids and its applications to stable rank of crossed products