  Let $k$ be a field of characteristic zero containing all roots of unity and
$K=k((t))$. We build a ring morphism from the Grothendieck group of
semi-algebraic sets over $K$ to the Grothendieck group of motives of rigid
analytic varieties over $K$. It extend the morphism sending the class of an
algebraic variety over $K$ to its cohomological motive with compact support. We
show that it fits inside a commutative diagram involving Hrushovski and
Kazhdan's motivic integration and Ayoub's equivalence between motives of rigid
analytic varieties over $K$ and quasi-unipotent motives over $k$ ; we also show
that it satisfies a form of duality. This allows us to answer a question by
Ayoub, Ivorra and Sebag about the analytic Milnor fiber.
