Discrete Symmetries In Lorentz-Invariant Non-Commutative QED

It is pointed out that the usual $\theta$-algebra assumed for non-commuting coordinates is not $P$- and $T$-invariant, unless one {\it formally} transforms the non-commutativity parameter $\theta^{\mu\nu}$ in an appropriate way. On the other hand, the Lorentz-covariant DFR algebra, which `relativitizes' the $\theta$-algebra by replacing $\theta^{\mu\nu}$ with a second-rank antisymmetric tensor operator $\htheta^{\mu\nu}$, is $C$-, $P$- and $T$-invariant. It is then proved that $C, P$ and $T$ are separately conserved in Lorentz-invariant Non-Commutative QED.