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You're right. Bill Fraser was the actor who played a soldier in a 1960s
tv show in the UK called 'The Army Game', so he'd fit in a similar role
in Ada. But he transforms into Broken-Arm Bill, who as you intuited,
means Shakespeare, because in Bend Sinister Nabokov alludes to the
First Folio engraving/portrait with two left arms, and of course for
the left arm to substitute for the right, it would
need to be broken.
"In March 1911, the "portrait" was submitted to the editor of 'The
Tailor and the Cutter' and 'The Gentleman's Tailor Magazine'. Both
these trade journals agreed that the figure was clothed in a coat
composed of the back and the front of the same left arm. This was
proved by cutting out the two halves of the coat and showing them
shoulder to shoulder." (from http://www.sirbacon.org/overlap.htm).
The "Roman deity" is the Catholic version of God. In Love's Labour's
Lost, Shakespeare uses the same device when he's speaking of a matter
concerning Catholics; Armado is lamenting the absence of decent
clothing, and that he's wearing rough wool against his skin; Boyet
"True, and it was enjoined him in Rome for want of linen.."
Shakespeare's religion is indeed a vexed subject. I personally enjoyed
the 1848 book by W. J. Birch that has WS as an atheist.
"... while Broken-Arm Bill prayed his Roman deity in a frenzy of fear
for the Tartar to finish his job and go. But, of course, an invaluable
detail in that strip of thought would have been â perhaps, next to
the pitcher peri â a glint, a shadow, a stab of Ardis.)" Why would
Broken-Arm Bill pray to a Roman deity?
Jansy Mello (again): Nabokov may have tried to mislead the reader into
thinking about Roman mythology, instead of perceiving that the "Roman
deity" is the Virgin Mary.
In this way, should Bill Fraser and Percy de Prey be related to the
Shakespeare controversies, Bill (Shakespeare?) would be seen as a
Catholic and not a Protestant, by our author.