diff --git a/src/KernelAbstractions.jl b/src/KernelAbstractions.jl
index 8ef7c071d..f2dda8d47 100644
--- a/src/KernelAbstractions.jl
+++ b/src/KernelAbstractions.jl
@@ -463,6 +463,17 @@ Adapt.adapt_storage(::ConstAdaptor, a::Array) = Base.Experimental.Const(a)
 
 constify(arg) = adapt(ConstAdaptor(), arg)
 
+# `constify` runs inside the kernel, where wrappers must be rebuilt without re-validating
+# them: Adapt.jl's rules for these wrappers go through constructors whose error paths build
+# strings, which does not compile for GPUs. Adapting only replaces the parent array, so the
+# existing fields remain valid.
+Adapt.adapt_structure(to::ConstAdaptor, A::Base.ReshapedArray) =
+    Base.ReshapedArray(adapt(to, parent(A)), size(A), A.mi)
+@eval function Adapt.adapt_structure(to::ConstAdaptor, A::PermutedDimsArray{T, N, perm, iperm}) where {T, N, perm, iperm}
+    P = adapt(to, parent(A))
+    return $(Expr(:new, :(PermutedDimsArray{eltype(P), N, perm, iperm, typeof(P)}), :P))
+end
+
 ###
 # Backend hierarchy
 ###
diff --git a/test/test.jl b/test/test.jl
index d0d3e1d07..f01fb6ccc 100644
--- a/test/test.jl
+++ b/test/test.jl
@@ -175,6 +175,11 @@ function unittest_testsuite(Backend, backend_str, backend_mod, BackendArrayT; sk
         @inbounds A[I] = B[I]
     end
 
+    @kernel function constarg2d(A, @Const(B))
+        i, j = @index(Global, NTuple)
+        @inbounds A[i, j] = B[i, j]
+    end
+
     @conditional_testset "Const" skip_tests begin
         let kernel = constarg(Backend(), 8, (1024,))
             # this is poking at internals
@@ -217,6 +222,25 @@ function unittest_testsuite(Backend, backend_str, backend_mod, BackendArrayT; sk
                 @test_skip false
             end
         end
+
+        # wrapped arrays are rebuilt around the constified array inside the kernel
+        host = Float32.(reshape(1:25, 5, 5))
+        dev = adapt(Backend(), host)
+        for (B, ref) in (
+                (vec(view(dev, 1:4, 1:4)), vec(view(host, 1:4, 1:4))),
+                (reshape(view(dev, 1:4, 1:4), 2, 8), reshape(view(host, 1:4, 1:4), 2, 8)),
+                (reshape(view(dev, :, 2:3), 2, 5), reshape(view(host, :, 2:3), 2, 5)),
+                (PermutedDimsArray(dev, (2, 1)), PermutedDimsArray(host, (2, 1))),
+            )
+            A = KernelAbstractions.zeros(Backend(), Float32, size(B))
+            if ndims(B) == 1
+                constarg(Backend(), 8)(A, B, ndrange = size(A))
+            else
+                constarg2d(Backend(), (4, 4))(A, B, ndrange = size(A))
+            end
+            synchronize(Backend())
+            @test Array(A) == ref
+        end
     end
 
     @kernel function kernel_val!(a, ::Val{m}) where {m}