I'm interested in exploring the following concept: people have discovered a certain kind of matter, let's call it "Unobtanium" (as it always goes).
Unobtanium actually has mass and is comprised of the known (to the day) elementary particles - albeit, perhaps, in some special conditions or combinations.
What is a special property I want to make "possible": if we add X kilograms of Unobtanium to Y kilograms of regular matter, the resulting substance mass is actually less than X+Y Also, I'm not referring to weight, I'm explicitly asking about mass.
My question: are there any known laws of physics today which will make it absolutely impossible, unless "magic"? To clarify: the answer "no, we do not know so far if mass manipulation is impossible" is a valid one.
I'm also not interested in destroying the matter, for which we already know about Antimatter. The impact on the matter to which Unobtanium was added should be as small as possible.
Bonus: If it's possible to explain that adding Unobtanium to the regular matter would (almost) completely nullify the resulting mass without (significantly) changing chemical properties of the substance.
Behind the scenes
The thing I'd like to achieve with this is the inertia reduction. Say, if we'd like to accelerate to 99.999% the speed of light very quickly provided that we have the tech to propel us that fast. Or to be able to do "very quick turns" during high velocity travels - normally it wouldn't be possible due to mass inertia which would not only prevent close to instant change of direction but also kill anything living due to insane G-Forces appearing in such circumstances.
This is also why mass and not weight, is what I'm aiming for.
EDIT: I'm not sure why it's "unclear what I'm asking" - especially given the fact that there are already 3 very good answers targeting exactly what I've asked :)