To a special embedding
Φ
\Phi
of circle algebras having the same spectrum, we associate an r-discrete, locally compact groupoid, similar to the Cuntz-Krieger groupoid. Its
C
∗
\mathbf {C}^*
-algebra, denoted
O
Φ
\mathcal {O}_{\Phi }
, is a continuous version of the Cuntz-Krieger algebras
O
A
\mathcal {O}_A
. The algebra
O
Φ
\mathcal {O}_{\Phi }
is generated by an AT-algebra and a nonunitary isometry. We compute its K-theory under the assumption that the AT-algebra is simple.