  We construct metric spaces that do not have property A yet are coarsely
embeddable into the Hilbert space. Our examples are so called warped cones,
which were introduced by J. Roe to serve as examples of spaces non-embeddable
into a Hilbert space and with or without property A. The construction provides
the first examples of warped cones combining coarse embeddability and lack of
property A.
  We also construct warped cones over manifolds with isometrically embedded
expanders and generalise Roe's criteria for the lack of property A or coarse
embeddability of a warped cone. Along the way, it is proven that property A of
the warped cone over a profinite completion is equivalent to amenability of the
group.
  In the appendix we solve a problem of Nowak regarding his examples of spaces
with similar properties.
