The most common and most likely answer to this crossword clue is the 9 letter word GLORIFIED
I've seen this crossword clue in The Daily Telegraph
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More clues leading to the result GLORIFIED
Buddy explains!

The straight part
We know that "inflated" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case inflated = glorified.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
Crossword Answer definitions
GLORIFIED adjective- Transformed into something glorious (often used sarcastically)
- To exalt, or give glory or praise to (something or someone).
- To make (something) appear to be more glorious than it is; regard something or someone as excellent baselessly.
- To worship or extol.