  We show how to construct counter-examples to the Hasse principle over the
field of rational numbers on Atkin-Lehner quotients of Shimura curves and on
twisted forms of Shimura curves by Atkin-Lehner involutions. A particular
example is the quotient of the Shimura curve X attached to the indefinite
rational quaternion algebra of discriminant 23*107 by the Atkin-Lehner
involution w107. The quadratic twist of X by Q(sqrt{-23}) with respect to this
involution is also a counter-example to the Hasse principle over Q.
