This example works using a new alpha databinding Autocomplete class and adaptor within the MvvmCross framework. It may be that these classes never actually make the cut to be full time framework members - in which case they can live in some external library instead.
The basic functionality uses databinding on 3 new properties:
PartialText - which is a partial text string - sent from the View to the ViewModel
ItemsSource - which is the set of current items available for the supplied PartialText - sent from the ViewModel to the View
SelectedObject - which is the current selected item - sent from the View to the ViewModel
Note that because of the Android threading model it is essential that every change in PartialText is met by an eventual signalled change in ItemsSource - and this should be a single change in object collection rather than lots of small changes.