  This paper is devoted to the study of Poincar\'e duality in K-theory for
general stratified pseudomanifolds. We review the axiomatic definition of a
smooth stratification $\fS$ of a topological space $X$ and we define a groupoid
$T^{\fS}X$, called the $\fS$-tangent space. This groupoid is made of different
pieces encoding the tangent spaces of the strata, and these pieces are glued
into the smooth noncommutative groupoid $T^{\fS}X$ using the familiar procedure
introduced by A. Connes for the tangent groupoid of a manifold. The main result
is that $C^{*}(T^{\fS}X)$ is Poincar\'e dual to $C(X)$, in other words, the
$\fS$-tangent space plays the role in $K$-theory of a tangent space for $X$.
