You obviously had a chat with him, Werner, since you are so well-informed about his last wishes :)
There is no written evidence for such a wish, at least none has been brought forward by the York supporters.
Historically, if you went into battle and were killed, at best you were buried on the battlefield. So, Bosworth would be a historically correct choice.
As to the chantry argument: Apart from his patronage of Queen's College, Cambridge, he was responsible for TEN other chantry houses which would therefore have equal “claim” to his body.
As to the argument that his relatives (after 500+ years) want him in York: They're relatives, that's all, none of them can claim to be a direct descendant – the only legitimate child of Richard died in childhood. His two illegitimate children seem to have died without issue.
Claims to his final resting place – that is, after this final resting place for 500+ years – could equally be brought forward by Fotheringhay Castle( his birthplace), Middleham (where he grew up), Gloucester (after all he was Duke of Gloucester before he became Duke of York) and Westminster Abbey (where his wife is buried, but also Henry VII who deposed him) amongst others. Dickie did move around quite a lot, you see.
There is no single location for the burial of pre-Reformation English Catholic monarchs, although since 1603 most monarchs of: England, and Scotland (1603–1707); of Great Britain (1707–1801); of United Kingdom (1801–present) have been buried in either Westminster Abbey or Windsor Castle.
The nearest Franciscan priory – for those arguing for a catholic burial similar to the original one at Greyfriars - would be in Nottingham.
York Uni had every chance to apply for the exhumation licence themselves and didn't. Now the work's done (and paid for), surprise surprise, York re-discovers its profound love for money… erm… the King.
By law, identifiable human remains have to be re-interred at the nearest consecrated graveyard, which would be Leicester Cathedral. And who would be the only cathedral in the UK with a monument to Richard III? That’s right… Leicester, not York.
Looking at some facts really helps to arrive at an opinion, doesn’t it?