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The present paper deals with the long-time asymptotic analysis of the initialvalue problem for the integrable defocusing nonlocal nonlinear Schr\"odingerequation $ iq_{t}(x,t)+q_{xx}(x,t)-2 q^{2}(x,t)\bar{q}(-x,t)=0 $ with astep-like initial data: $q(x,0)\to 0$ as $x\to -\infty$ and $q(x,0)\to A$ as$x\to +\infty$. Since the equation is not translation invariant, the solutionof this problem is sensitive to shifts of the initial data. We consider afamily of problems, parametrized by $R>0$, with the initial data that can beviewed as perturbations of the "shifted step function" $q_{R,A}(x)$:$q_{R,A}(x)=0$ for $x<R$ and $q_{R,A}(x)=A$ for $x>R$, where $A>0$ and $R>0$are arbitrary constants. We show that the asymptotics is qualitativelydifferent in sectors of the $(x,t)$ plane, the number of which depends on therelationship between $A$ and $R$: for a fixed $A$, the bigger $R$, the largernumber of sectors. Moreover, the sectors can be collected into 2 alternategroups: in the sectors of the first group, the solution decays to 0 while inthe sectors of the second group, the solution approaches a constant (varyingwith the direction $x/t=const$).

Defocusing nonlocal nonlinear Schr\"odinger equation with step-like boundary conditions: long-time behavior for shifted initial data