Elemental Forums
It appears that all armor bought in item shop that is from defense research can not be equipped by any unit. When attempting to equip the armor piece the error dialog 'Can't Equip Leather Helm doesn't fit this unit'. It does use the correct name for all armor pieces I tried.
Are you trying to equip the purchased items on regular units or on your sovereign/heroes? Only the latter can use bought/quested items.
I bought the +1 movement boots in one of my games and I tried to equip them on my sovereign and it sound this unit can not equip this item.
Having the same problem trying to equip a quest item on my sovereign (Azur's Armor)
See here for screen shot, saved game, and sovereign xml
Had noted this with the Journeymans cloak another game. I could however equip a full set of leather armor bought from the shop.
Unfortunately that game was on a different machine, so no save and err. Will report back if i got an according savegame.
Here is the promised Savegame where (for me) the souvereign can not equip helm, back and full leather armor.
http://dl.dropbox.com/u/9038574/Thingsnotfitting.EleSav
As the Screenshot below also shows, the items are also not listed in his detailed inventory, while they appear in the quick access bar to the bottem left.
Is there a chance you have to remove the robe first? so.. could you equip leather armor, -then- a helm?
The back does not share an itemslot with the robe so it seems unlikely. However as the robe is my starting equipment, i can not even unequip it. It should simply be replaced if an corresponding item is equipped, and be restored if the item is uneqiupped again.
I also have been unable to equip the Travelers Boots and Leather Armor on either my sovereign or heroes. Wish I'd known that before I bought them at the store!
Had to say...Sodol? You mean..Palpatine right 
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