We construct a smoothed version of the Toeplitz extension for a
C
∗
{C^ * }
-dynamical system
(
A
,
α
,
R
)
(A,\alpha ,{\mathbf {R}})
. It defines a Thom class
[
τ
]
[\tau ]
in
K
K
1
(
A
,
A
×
α
R
)
K{K^1}(A,A{ \times _\alpha }{\mathbf {R}})
. The Wiener-Hopf-Rieffel extension for
(
A
,
α
,
R
)
(A,\alpha ,{\mathbf {R}})
is shown to be a smoothed Toeplitz extension which is the
K
K
KK
-inverse of
[
τ
]
[\tau ]
.