Abstract: Let $X$ be a complex affine variety with an action of a torus $T$, and an attractive fixed point $x_0$. We say that $X$ is a rational cell if $H^{2n}(X,X-\{x_0\})=\mathbb{Q}$ and $H^{i}(X,X-\{x_0\})=0$ for $i\neq 2n$, where $n={\rm dim\,}_{\mathbb{C}}(X)$. These objects appear naturally in the study of group embeddings. A fundamental result in equivariant cohomology asserts that the transgression ${\bf Eu}_T \in H^{2n}(BT)$ of a generator of $H^{2n}(X,X-\{x_0\})$ splits into a product of singular characters, ${\bf Eu}_T={\chi_1}^{k_1}\ldots {\chi_m}^{k_m}$. This characteristic class is by definition the Equivariant Euler class of $X$ at $x_0$. Loosely speaking, one could think of $X$ as a sort of $T$-vector bundle over a point. My goal in this talk is to make this claim precise, and to show why one could hope to build similar elements in equivariant $K$-theory, i.e. Bott classes, by using localization and completion techniques. This is work in progress.