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We show that despite the inherent non-locality of quantum field theories on the Groenewold-Moyal (GM) plane, one can find a class of ${\bf C}$, ${\bf P}$, ${\bf T}$ and ${\bf CPT}$ invariant theories.
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A. P. Balachandran, A. Pinzul and S. Vaidya, Spin and Statistics on the Groenewold-Moyal Plane: Pauli-Forbidden Levels and Transitions
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A. P. Balachandran, A. Pinzul and B. A. Qureshi, UV-IR Mixing in Noncommutative Plane
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A. P. Balachandran, T. R. Govindarajan, G. Mangano, A. Pinzul, B. A. Qureshi, S. Vaidya, Statistics and UV-IR Mixing with Twisted Poincare Invariance
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A. P. Balachandran, A. R. Queiroz, A. M. Marques, P. Teotonio-Sobrinho, Deformed Kac-Moody and Virasoro Algebras
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M. Dimitrijevic and J. Wess, Deformed Bialgebra of Diffeomorphisms
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A. P. Balachandran, A. Pinzul and A. R. Queiroz, in preparation
Cited in the paper.