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I am interested in the K-theory of the Bohr compactification $\mathbb{R}_B$ of the real numbers.

Do we have $K_0(C(\mathbb{R}_B))$ isomorphic to $K_1(C(\mathbb{R}_B))$ ?

More generally, what do we know about these groups ? Have they been determined ?

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What is $C(-)$? –  Fernando Muro Jan 20 '12 at 10:52
By $C(X)$, I mean the algebra of continuous functions from $X$ to $\mathbb{C}$. –  Oliver Jan 23 '12 at 5:07
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