A motive over a field is of abelian type if it belongs to the thick and
rigid subcategory of Chow motives spanned by the motives of abelian varieties
over . This paper contains three sections of independent interest. First, we
show that a motive which becomes of abelian type after a base field extension
of algebraically closed fields is of abelian type. Given a field extension
and a motive over , we also show that is finite-dimensional if
and only if is finite-dimensional. As a corollary, we obtain
Chow--Kuenneth decompositions for varieties that become isomorphic to an
abelian variety after some field extension. Second, let be a universal
domain containing . We show that Murre's conjectures for motives of abelian
type over reduce to Murre's conjecture (D) for products of curves over
. In particular, we show that Murre's conjecture (D) for products of
curves over implies Beauville's vanishing conjecture on abelian
varieties over . Finally, we give criteria on Chow groups for a motive to be
of abelian type. For instance, we show that is of abelian type if and only
if the total Chow group of algebraically trivial cycles
is spanned, via the action of correspondences, by the Chow groups of products
of curves. We also show that a morphism of motives , with
Kimura finite-dimensional, which induces a surjection also induces a surjection on homologically trivial cycles.