There are several abilities that deal damage after an amount of time (Zed's ultimate, Karthus' ultimate, Zileans' time bomb etc). While waiting for the damage to trigger, if the champion is exhausted will the damage be reduced by 40%?
Exhaust affects the damage when it hits.
So if you exhaust Karthus (2.5sec), then he casts his ult (3sec) the utl will impact with full damage and is not affected by exhaust.
So if Karthus casts his ult (3sec) and you exhaust him when he already channled for 1 sec the utl will impact with reduced damage.
Since exhaust reduces Movement Speed and Attack Speed by 30%, enemies Armor and Magic Resist by 10, and their damage dealt by 40%. Heal (Zilean ult) is not affected.