King invests American subject with decoration (7)
I believe the answer is:
macbeth
'king' is the definition.
(I know that Macbeth is a king)
'subject with decoration' is the wordplay.
'subject' becomes 'math' (math is a kind of subject).
'with' indicates putting letters inside.
'decoration' becomes 'cbe' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'math' going around 'cbe' is 'MACBETH'.
'invests american' acts as a link.
This may not be correct. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for macbeth that I've seen before include "its name must not be mentioned" , "King of Scotland, 1040-1057" , "In sleep murderer" , "He doth murder sleep (Shak.)" , "piece" .)