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We consider an array of dual-core waveguides, which represent an opticalrealization of a chain of dimers, with an active (gain-loss) coupling betweenthe cores, opposite signs of discrete diffraction in the parallel arrays, and aphase-velocity mismatch between them (which is necessary for the stability ofthe system). The array provides an optical emulation of the charge-parity($\mathcal{CP}$) symmetry. The addition of the intracore cubic nonlinearitygives rise to several species of fundamental discrete solitons, which exist incontinuous families, although the system is non-Hermitian. The existence andstability of the soliton families are explored by means of analytical andnumerical methods. An asymptotic analysis is presented for the case of weakintersite coupling (i.e., near the anticontinuum limit), as well as weakcoupling between cores in each dimer. Several families of fundamental discretesolitons are found in the semi-infinite gap of the system's spectrum, that haveno counterparts in the continuum limit, as well as a branch which belongs tothe finite band gap and carries over into a family of stable gap solitons inthat limit. One branch develops an oscillatory instability above a criticalstrength of the intersite coupling, others being stable in their entireexistence regions. Unlike solitons in conservative lattices, which arecontrolled solely by the strength of the intersite coupling, herefundamental-soliton families have several control parameters, one of which,viz., the coefficient of the intercore coupling in the active host medium, maybe readily adjusted in the experiment by varying the gain applied to themedium.

Solitons in a chain of charge-parity-symmetric dimers