  We present the construction of an associative, commutative algebra $\hat
{\mathcal G}$ of generalized functions on a manifold $X$ satisfying the
following optimal set of permanence properties:
  (i)The space of distributions on $X$ is linearly embedded into $\hat
{\mathcal G}$, $f(p)\equiv 1$ is the unity in the algebra.
  (ii) For every smooth vector field $\xi$ on $X$ there exists a derivation
operator $\hat L_\xi: \hat {\mathcal G} \to \hat {\mathcal G}$ which is linear
and satisfies the Leibniz rule.
  (iii) $L_\xi$ restricted to the space of distributions on $X$ is the usual
Lie derivative.
  (iv) Multiplication in the algebra restricted to the space of smooth
functions is the usual (pointwise) product of functions.
  Moreover, the basic building blocks of $\hat {\mathcal G}$ are defined in
purely intrinsic terms of the manifold $X$.
