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In this note we present a complete computation of the topological K-theory ofthe reduced C*-algebra of a semidirect product of the form$\Gamma=\mathbb{Z}^n\rtimes_\rho\mathbb{Z}/2$ with no further assumptions aboutof the conjugacy action $\rho$. For this, we use some results for$\mathbb{Z}/2$-equivariant K-theory proved by Rosenberg and previous results ofDavis and Luck when the conjugacy action $\rho$ is free outside the origin.

The topological K-theory of crystallographic groups with holonomy $\mathbb{Z}/2$