name of the book and author published about 5 years ago in english about
the incorporation of earlier local religious and cultural practices
and thought into islam and how that produced local variations in islam

That is a pretty broad area being covered. Islam during what period in
its evolution? (a general range of half a millenium would suffice)
What 'local' are you talking about? Morocco? Saudi Arabia? Somewhere
else? What *kind* of variations in Islam? Are you thinking of actual
'denominations', such as Sunni and Shi'ite? Or, perhaps, simply
theological variations of a minor sort?