diff --git a/loopy/schedule/tools.py b/loopy/schedule/tools.py
index f2164b6dd..8c196e205 100644
--- a/loopy/schedule/tools.py
+++ b/loopy/schedule/tools.py
@@ -30,6 +30,7 @@
 
 from loopy.kernel.data import AddressSpace, TemporaryVariable, ArrayArg
 from loopy.kernel import LoopKernel
+from loopy.isl_helpers import static_min_of_pw_aff
 
 
 # {{{ block boundary finder
@@ -381,6 +382,23 @@ def _check_for_access_races(map_a, insn_a, map_b, insn_b, knl, callables_table):
             if dt == isl.dim_type.in_:
                 tag, = filter_iname_tags_by_type(knl.inames[name].tags,
                                                  HardwareConcurrentTag)
+                if any(not aff.plain_is_zero()
+                       for _, aff in (knl
+                                      .get_iname_bounds(name)
+                                      .lower_bound_pw_aff
+                                      .get_pieces())
+                       ):
+                    # Non-zero hardware inames are offseted in loopy's codegen. See
+                    # https://github.com/inducer/loopy/issues/600#issuecomment-1104066735
+                    # => Accordingly offset the access maps
+                    lbound_val = (static_min_of_pw_aff(knl
+                                                       .get_iname_bounds(name)
+                                                       .lower_bound_pw_aff,
+                                                       constants_only=True)
+                                  .get_constant_val().to_python())
+                    map_ = map_.apply_domain(
+                            isl.Map(f"{{[{name}] -> [{name}-{lbound_val}]}}"))
+
                 map_ = map_.set_dim_name(dt, pos, str(tag))
 
         for i_l in lsize: