On $K_0$-Groups for Substitution Tilings

Abstract

The group $C(\Om,\Z)/\E$ is determined for tilings which are invariant under a locally invertible primitive \sst\ which forces its \saum. In case the tiling may be obtained by the generalized dual method from a regular grid this group furnishes part of the $K_0$-group of the algebra of the tiling. Applied to Penrose tilings one obtains $K_0(\A_\tl)=\Z^8\oplus\Z$.