  We extend the notion of the cardinality of a discrete groupoid (equal to the
Euler characteristic of the corresponding discrete orbifold) to the setting of
Lie groupoids. Since this quantity is an invariant under equivalence of
groupoids, we call it the volume of the associated stack rather than of the
groupoid itself. Since there is no natural measure in the smooth case like the
counting measure in the discrete case, we need extra data to define the volume.
This data has the form of an invariant section of a natural line bundle over
the groupoid. Sections of a square root of this line bundle constitute an
"intrinsic Hilbert space" of the stack.
