Let $G$ be a countable discrete group. Let the complex group ring $/C[G]$ act on the space of $/ell^p$ functions (for finite $p$) on $G$ by convolution, and denote by $B^p(G)$ its operator completion. $G$ is said to have Haagerup property if it admits a proper affine isometric action on a Hilbert space. $G$ is said to have the property of rapid decay if its weighted square integrable functions form an algebra. We prove that if G possesses these two properties, the K theory of $B^p(G)$ does not depend on the parameter p.

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