We compute the K‐groups of the ‐algebra of bounded operators generated by the Boutet de Monvel operators with classical SG‐symbols of order (0,0) and type 0 on , as defined by Schrohe, Kapanadze and Schulze. In order to adapt the techniques used in Melo, Nest, Schick and Schrohe's work on the K‐theory of Boutet de Monvel's algebra on compact manifolds, we regard the symbols as functions defined on the radial compactifications of and . This allows us to give useful descriptions of the kernel and the image of the continuous extension of the boundary principal symbol map, which defines a ‐algebra homomorphism. We are then able to compute the K‐groups of the algebra using the standard K‐theory six‐term cyclic exact sequence associated to that homomorphism.